FWPRDC Project PN04.2005 Maximising impact sound resistance of timber framed floor/ceiling systems
Final Report By Hyuck Chung, George Dodd, Grant Emms, Ken McGunnigle, Gian Schmid.
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The opinions provided in the Report have been prepared for the Client and its specified purposes. Accordingly, any person other than the Client uses the information in this report entirely at its own risk. The Report has been provided in good faith and on the basis that every endeavour has been made to be accurate and not misleading and to exercise reasonable care, skill and judgment in providing such opinions. Neither the New Zealand Pine Manufacturers Association, nor any of its employees, contractors, agents nor other persons acting on its behalf or under its control accept any responsibility or liability in respect of any opinion provided in this Report by the New Zealand Pine Manufacturers Association.
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FWPRDC PN04.2005
Maximising impact sound resistance of timber framed floor/ceiling systems
Prepared for the Forest & Wood Products Research and Development Corporation by
Hyuck Chung, George Dodd, Grant Emms, Ken McGunnigle, Gian Schmid.
January 2006 THE FWPRDC IS JOINTLY FUNDED BY THE AUSTRALIAN FOREST AND WOOD PRODUCTS INDUSTRY AND THE AUSTRALIAN GOVERNMENT
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The Researchers (and their helpers). • • • •
• • •
Hyuck Chung – PhD (Mathematics–Auckland) – Post Doctoral Fellow, Auckland University. George Dodd – PhD (Acoustics – Southampton) – Senior Lecturer, Auckland University. Grant Emms – PhD (Acoustics–Auckland) – Scientist at Scion, New Zealand. Ken McGunnigle – MSc(Zoology), (MRICS Chartered Surveyor (QS), MCIOB Chartered Builder, MNZIQS Member NZ Institute of Quantity Surveyors, BRANZ Accredited Adviser, MNZIBS, Registered Building Surveyor, MNZIOB Member of NZ Institute of Building) – Building and building acoustics consultant at Prendos, New Zealand. Gian Schmid – Acoustics Technician at Auckland University. Murray Hollis – Electronics Technician at Auckland University. Students at the Acoustics Research Centre (Arif, Fady, Ming)
The Industry Partners. • • • •
Carter Holt Harvey (Warwick Banks, Hank Bier) CSR (Keith Nicholls, Bill Thompson) Tenon (Bill Burbridge, Scott Stratton) Winstone Wallboards (Rob Hallows).
Project Administration. •
New Zealand Pine Manufacturers’ Association (Lawrie Halkett)
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Executive Summary. Current occupier perception of timber inter-tenancy floor/ceiling systems used in Australasia is that they do not perform acoustically as well as heavy masonry building systems, particularly in terms of impact sound transmission from the floor above. This perception has resulted in a limit in growth of multi-residential timber apartments in Australasia. Concern for this problem and an expectance of a growth in medium-rise apartment construction has resulted in increased Australasian research into this problem. This concern is not unique to Australasia, and as a result, a number of other countries with an interest in timber housing construction have also been researching this problem. A team of New Zealand building acoustics researchers and Australasian companies formed a consortium to tackle this project. This project essentially consisted of progressing existing Australasian and overseas research into this problem with a view to produce floor/ceiling system design recommendations for floors having acoustic properties which are comparable with concrete floor constructions, while also meeting the acoustic requirements of the Australian and New Zealand building code, and being cost effective and buildable using existing construction industry skills. The expected project outputs (deliverables) of the project were design recommendations for timber-based, inter-tenancy floor/ceiling systems to enable them to have an impact sound insulation performance which complies with the proposed Acoustic Regulations of the BCA and which is equal to or better than that of a 150mm concrete slab floor. It has been found by experience from all over the world that inter-tenancy lightweight floors tend to be regarded as poor performers by occupiers in the neighbouring tenancy (usually the tenancy below). This poor performance is often expressed by occupiers as the hearing of ‘bumps and thumps’ from above and is due to poorer low-frequency impact insulation. As a result of this understanding the project has focussed on the issue of lowfrequency impact insulation. To achieve the project outputs the project was divided up into a number of aspects, with the focus being on low-frequency impact insulation performance:- Theoretical modelling, - Experimental testing, - Subjective testing. The theoretical modelling involved the development of an analytical model to describe the low-frequency impact insulation performance of a timber floor and the effect a room has on the sound produced by such a floor. The resulting model was novel in many respects, and will be published in international journals. The model was used to predict the performance of a timber floor when certain parametric changes were made to it. This produced a number of results and conclusions which can be used as a basis for design recommendations. The experimental testing programme involved the building and testing of 25 floor designs in a laboratory room designed for the purpose. The experimental testing consisted of low-frequency vibration measurements of the floor upper surface and the ceiling, as well as higher frequency measurements using standard procedures. The results of the low-frequency measurements were very detailed and were used to help develop and to validate the theoretical model, as well as enabling detailed performance comparisons of the tested floors. The subjective testing programme consisted of recording the sounds made by various impacts on a selection of the experimentally tested floors. These sounds along with impact sounds from a 150mm thick concrete floor were then played back to 30 subjects in a listening room. The listening room was made to be like a living room. The subjects were asked which Page 5
floor they would prefer to live with given the sounds they heard. The technique used in this procedure was a novel refinement of previous, similar subjective tests. The results of this subjective testing showed that it was possible for a timber floor to perform as well as a 150mm concrete floor. The results also showed that it was possible to correlate performance with the loudness of the impact sounds. The results of the theoretical modelling, experiment and subjective testing produced conclusions which enabled design recommendations to be made to produce a timber floor with low-frequency performance equal to a concrete floor. The main design recommendations consisting of adding mass and vibration damping to the floor upper surface in the form of a granular material (consisting of a sand/sawdust mix), using independent ceiling joists to further insolate the ceiling from the rest of the floor, and making the ceiling heavier. These design recommendations could be used in isolation or together to produce a floor with effective lowfrequency impact insulation.
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Preface. The printed version of this report has been divided into two volumes. The first volume contains the primary discussion and analysis. The second volume contains raw results, useful diagrams and photographs. The idea is that when referring to the first volume one can also refer to the second volume for relevant supporting information. References have been divided up on a chapter by chapter basis, and are located in the final section of each chapter. These are referred to in the text by way of author surname and year of publication (if necessary). The first chapter is a somewhat self-contained overview of the project. It is a good idea to read this chapter first, and then to refer to the indicated chapters.
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Volume I
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Table of Contents. 1
PROJECT OVERVIEW........................................................................................13 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
INTRODUCTION.....................................................................................................................13 OVERVIEW OF THE ISSUES. ...............................................................................................13 OVERVIEW OF EXISTING KNOWLEDGE. ...........................................................................15 THE STRUCTURE OF THE RESEARCH PROJECT. ...........................................................18 CONCLUSIONS OF THE ANALYSES. ..................................................................................19 SUCCESSFUL FLOOR DESIGNS. ........................................................................................22 SUGGESTIONS FOR FURTHER WORK...............................................................................26 TECHNOLOGY TRANSFER OF OUTPUTS. .........................................................................27 REFERENCES........................................................................................................................28
2 OVERVIEW OF EXISTING FLOOR SYSTEM DESIGNS AND RECENT RESEARCH RESULTS...............................................................................................29 2.1 2.2 2.3 2.4 2.5
3
THEORETICAL MODELLING OF A JOIST FLOOR. ...........................................39 3.1 3.2 3.3 3.4 3.5 3.6 3.7
4
INTRODUCTION...................................................................................................................125 EXAMINATION OF THE LOW-FREQUENCY RESULTS ....................................................125 EXAMINATION OF THE HIGH-FREQUENCY RESULTS. ..................................................144 BRIEF EXAMINATION OF THE VIBRATION WAVEFORMS OBSERVED. ........................145 REFERENCES......................................................................................................................158
SUBJECTIVE LISTENING TESTS AND ASSESSMENTS ................................159 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11
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INTRODUCTION.....................................................................................................................77 SINGLE FIGURE RATINGS. ..................................................................................................77 150MM CONCRETE REFERENCE FLOOR. .........................................................................81 FLOOR JOIST PROPERTIES ................................................................................................83 FLOOR UPPER LAYER PROPERTIES .................................................................................91 CAVITY AND CEILING CONNECTION PROPERTIES .........................................................99 CEILING PROPERTIES .......................................................................................................109 EFFECTS OF FLOOR SPAN AND ROOM SIZE. ................................................................117 CONCLUSIONS OF THE TREND ANALYSIS. ....................................................................123 REFERENCES......................................................................................................................124
ANALYSIS OF EXPERIMENTAL RESULTS .....................................................125 5.1 5.2 5.3 5.4 5.5
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INTRODUCTION.....................................................................................................................39 PART I: REVIEW OF EXISTING MODELS ............................................................................40 PART II: OUR MODELLING FOR LTF FLOOR SYSTEMS ...................................................50 MODELLING FIBROUS INFILL. .............................................................................................59 FURTHER COMPARISON OF THE FLOOR MODEL WITH EXPERIMENTAL RESULTS...61 PART III: MODELLING THE RECEIVING ROOM..................................................................71 REFERENCES........................................................................................................................73
FLOOR MODEL ANALYSIS ................................................................................77 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10
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INTRODUCTION.....................................................................................................................29 EXISTING LOW-FREQUENCY PERFORMANCE UNDERSTANDING. ...............................29 EXISTING HIGH-FREQUENCY PERFORMANCE UNDERSTANDING................................30 EXISTING LIGHTWEIGHT FLOOR COMPONENTS IN USE AROUND THE WORLD. .......31 REFERENCES........................................................................................................................37
INTRODUCTION...................................................................................................................159 SUBJECTIVE VERSUS OBJECTIVE TESTING ..................................................................160 PREVIOUS RESEARCH ON SUBJECTIVE ACCEPTABILITY ...........................................160 IEC LISTENING ROOM ........................................................................................................162 OBJECTIVE EVALUATION OF PERFORMANCE ...............................................................163 EXPERIMENTAL SETUP .....................................................................................................164 THE SUBJECTS AND THEIR TASK ....................................................................................166 RESULTS AND DISCUSSION .............................................................................................167 WALKING ON BARE FLOOR...............................................................................................167 REFERENCES......................................................................................................................172 QUESTIONNAIRES USED IN THE SUBJECTIVE TESTING ..............................................174
LOW-FREQUENCY MEASUREMENT RESULTS.............................................187 7.1 7.2 7.3
INTRODUCTION...................................................................................................................187 EXPERIMENTAL SETUP. ....................................................................................................187 EXPERIMENTAL TECHNIQUE. ...........................................................................................191
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7.4 7.5 7.6 7.7
8
EXPERIMENTAL RESULTS OVERVIEW ........................................................................... 191 3-DIMENSIONAL VIBRATION PLOTS ................................................................................ 192 AVERAGE SURFACE VELOCITY PLOTS .......................................................................... 192 REFERENCES..................................................................................................................... 234
HIGH-FREQUENCY MEASUREMENT RESULTS............................................ 235 8.1 8.2
SUMMARY OF THE MEASUREMENT OF IMPACT SOUND INSULATION OF FLOORS.235 THE RESULTS FOR EACH MEASURED FLOOR. ............................................................. 236
9 FLOOR COST COMPARISON. ......................................................................... 255 10 PROPERTIES OF MATERIALS USED.......................................................... 258 10.1 10.2 10.3 10.4 10.5
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PANEL PRODUCTS: ........................................................................................................... 258 POURED-ON TOPPINGS/SCREEDS. ................................................................................ 258 JOISTS. ................................................................................................................................ 258 INFILL MATERIALS. ............................................................................................................ 259 CEILING FIXTURES. ........................................................................................................... 259
FLOOR DIAGRAMS AND PHOTOGRAPHS ................................................. 260
11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 11.12 11.13 11.14 11.15 11.16 11.17 11.18 11.19 11.20 11.21 11.22 11.23 11.24 11.25 11.26 11.27
THE TEST CHAMBER. ........................................................................................................ 260 REFERENCE CONCRETE FLOOR (FLOOR 0). ................................................................ 262 FLOOR 2. ............................................................................................................................. 263 FLOOR 3 .............................................................................................................................. 269 FLOOR 4 .............................................................................................................................. 271 FLOOR 5. ............................................................................................................................. 272 FLOOR 6 .............................................................................................................................. 274 FLOOR 7 .............................................................................................................................. 275 FLOOR 8 .............................................................................................................................. 278 FLOOR 9.......................................................................................................................... 281 FLOOR 10........................................................................................................................ 282 FLOOR 11........................................................................................................................ 284 FLOOR 12........................................................................................................................ 286 FLOOR 13........................................................................................................................ 290 FLOOR 14........................................................................................................................ 292 FLOOR 15........................................................................................................................ 293 FLOOR 16........................................................................................................................ 298 FLOOR 17........................................................................................................................ 299 FLOOR 18........................................................................................................................ 301 FLOOR 19........................................................................................................................ 303 FLOOR 20........................................................................................................................ 304 FLOOR 21........................................................................................................................ 313 FLOOR 22........................................................................................................................ 314 FLOOR 23........................................................................................................................ 316 FLOOR 24........................................................................................................................ 317 FLOOR 25........................................................................................................................ 320 FLOOR 26........................................................................................................................ 321
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1 PROJECT OVERVIEW. 1.1
INTRODUCTION.
Current occupier perception of timber inter-tenancy floor/ceiling systems used in Australasia is that they do not perform acoustically as well as heavy masonry building systems, particularly in terms of impact sound transmission from the floor above. This perception has resulted in a limit in growth of multi-residential timber apartments in Australasia. Concern for this problem and an expectance of a growth in medium-rise apartment construction has resulted in increased Australasian research into this problem. This concern is not unique to Australasia, and as a result, a number of other countries with an interest in timber housing construction have also been researching this problem. A team of New Zealand building acoustics researchers and Australasian companies formed a consortium to tackle this project. This project essentially consisted of progressing existing Australasian and overseas research into this problem with a view to produce floor/ceiling system design recommendations for floors having acoustic properties which are comparable with concrete floor constructions, while also meeting the proposed Australian and New Zealand building code requirements, and being cost effective and buildable using existing construction industry skills. The members of the team consist of acoustic professionals and researchers, mathematicians, construction experts, structural engineers, and people expert in the area of bringing new construction ideas and techniques to the market place. In some instances the researchers have both acoustic and practical building experience. It is this breadth of knowledge of the research team which tends to set this team apart from others, giving a practical grounding to the development of their ideas. The project outputs (project brief). The brief for this project is encapsulated in the expected outputs (deliverables) of the project contract: “The expected output will be design recommendations for timber-based, inter-tenancy floor/ceiling systems to enable them to have an impact sound insulation performance which complies with the proposed Acoustic Regulations of the BCA and which is equal to or better than that of a 150mm concrete slab floor.” 1.2
OVERVIEW OF THE ISSUES.
The aim of the project. The aim or brief of the project can be divided into two aspects:1) Achieving the appropriate mid to high frequency floor impact insulation performance. 2) Achieving the appropriate low-frequency floor impact insulation performance. Aspect (1) concerns the frequency range from about 100Hz to 3150Hz, and can be reasonably well determined and rated1 by standard impact insulation measurement techniques (e.g. following standard ISO 140) and the resulting single figure ratings (e.g. following standard ISO 717). According to the BCA Acoustic Regulations (which have subsequently come into force) a floor’s mid to high-frequency performance should be such that Ln,w+CI is less than or equal to 62 dB. As far as almost any type of inter-tenancy floor is concerned this is relatively 1
Reasonably well determined and rated means that the measurements are accurate and the resulting values, particularly the single figure ratings, are related to people’s perceptions and subjective responses. Page 13
easily achieved by putting the appropriate resilient surface or underlay on the subfloor. It is often the case that timber floors, due to their inherently softer materials, have a head start here over concrete floors. Aspect (2) concerns the frequency range below about 100 to 200Hz. It is in this lowfrequency range that problems arise in a number of areas. For one thing, this is the area that lightweight floor systems have problems compared to heavy floor systems due to, well, their light weight and perhaps their lower stiffness. It has been found by experience over the world that inter-tenancy lightweight floors tend to be regarded as poor performers by occupiers in the neighbouring tenancy (usually the tenancy below). This poor performance is often expressed by occupiers as the hearing of ‘bumps and thumps’ from above and is due to poorer lowfrequency impact insulation. In part, this has presumed to have been caused by people walking or otherwise moving around on the floor above. Another contribution to these low-frequency ‘bumps and thumps’ can be things such as doors closing or heavier objects being dropped. On the other hand, heavy masonry systems, from experience, appear to perform ‘acceptably’ in this area of low-frequency impact insulation. Another problem with low-frequency impact insulation of floors is that it is difficult to measure and rate. It is difficult to measure the low-frequency performance of a floor due to the fact that the room connected to the floor has a significant contribution to the floors’ performance and it is difficult to remove this effect for low-frequencies. It is also difficult to rate the low-frequency performance of a floor because we don’t really understand how objective measurements relate to people’s perceptions of the low-frequency impact insulation of a floor. Due to the uncertainty surrounding how one can express and rate low-frequency performance, and because of the appreciation that heavy masonry floors seem to perform acceptably in the minds of occupiers, the measure of acceptable low-frequency performance is to make such performance comparable to a 150mm dense concrete slab floor (as stated in the objective). Note that in the above paragraphs on low-frequency floor performance, only lightweight floors were mentioned, rather that lightweight timber floors specifically. This is simply because the problem is not specific to timber floors, and is suffered by other lightweight systems, even thin, lightweight or hollow-core concrete slabs. Both low and high frequency aspects of impact insulation are important. However, the problem of low-frequency impact insulation is the one which is most challenging to solve for lightweight floor systems, and hence will received the most attention in this project. This is not to say that the high-frequency impact insulation of a floor is not important, but it is something which is relatively easy to deal with and measure, having received much attention from researchers and industry. Summary of the Problems. The problem of the impact insulation performance of floors can be divided into a number of factors which influence the overall result; these are illustrated in Figure 1-1. The first factor is the impact source itself. The issue here is knowing which impact sources represent activities that happen in apartments, or at least, ultimately produce a result which ranks floors according to the occupiers’ opinions. The second factor is the reaction of the floor to impact forces imposed on it. The reaction we are primarily concerned with is how the ceiling of the floor vibrates in response to the impact forces. The issue here is to produce floor designs which minimise the ceiling vibrations which produce offending sounds for the impacts that typically occur in apartments. The third factor is the influence of the room on the sound generated by the ceiling vibrations. It is important to realise that the so-called receiving room itself is a highly influential factor in sounds that are produced by the ceiling vibrations. This is particularly so for low-frequency sounds. Page 14
The fourth factor is the psychoacoustic response of the occupants in the receiving room below the floor. This factor is how the occupiers react to the sounds that are produced in the receiving room. This subjective aspect of the problem is important to determine how well floors and sounds generated by impacts on them perform against each other and against some reference (i.e. how they can be ranked). This is possibly the most important factor of the problem, but is also possibly the most nebulous.
Impact source
Floor reaction to applied force
Influence of room on sound generated
Psychoacoustic response
Figure 1-1. Diagram illustrating the breakdown of the problem into factors influencing the outcome.
1.3
OVERVIEW OF EXISTING KNOWLEDGE.
The problem of low-frequency impact sound insulation in light-weight timber floors has been an issue for a long time. In recent years, research and anecdotal evidence have identified the problem as being of major concern for customers. In particular, the increased acceptance and use of light timber-framed construction in various parts of the world has highlighted the issues in certain countries (for example, in the US Blazier and DuPree (1994) highlighted increased customer perception of low-frequency impact sounds). As a result, a number of research projects have looked into this issue. Probably the most significant research project into this area was done in Scandinavia, by Finland, Sweden, Norway and Denmark. As part of the so-called Nordic R&D project “Multistorey timber frame buildings”, the project consisted of each contributing country selecting a number of suitable floors (after some experimental development), and then installing these floors into real building developments with occupants. This project spanned 5 years and finished in 1999. A number of summary papers have been completed by the main researchers into this project, a good one being that produced by Hveem (1998), the principal researcher of this project. Existing Low-frequency Performance understanding. The results of the Nordic R&D project resulted in a number of conclusions and desires for further work. It is worth summarising their conclusions here, because they seem to be a set of effective conclusions about the problem – echoing conclusions of other research projects. Hveem (1998) produced these conclusions:-
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• •
• • • •
There is a trend against stiffer joist construction in the form of deeper joists, i.e. the fundamental frequency shouldn’t be too high. This echoed by Blazier and DuPree (1994). Lightweight floating floor systems (e.g. a couple of layers of particleboard on 20mm mineral wood board) don’t improve impact insulation below 160Hz. Even heavyweight floating floor systems (e.g. 50mm dense concrete on 20mm mineral wool board) won’t improve low-frequency performance below 50Hz, at best. The elastic suspended ceiling systems they used perform well, but have a resonance frequency of about 30Hz, and hence have limitations. Completely filling (or, even overfilling) the cavity with mineral wool has a positive effect on performance, especially for the cavity depths found in floors. For the low-frequency range it is important to separate the most dominating natural frequencies in the floor system from the modes in the room, given by typical dimensions. The peak energy of a footfall occurs in the frequencies below 50Hz.
Sipari (2000), the leader of the Finnish contribution to the acoustic aspect of the Nordic R&D project, concluded that the way forward is to increase mass and stiffness of the floor and floor parts. They found in their testing that a composite floor consisting of concrete slab bound to joists, so that they structurally work together, is an effective solution. They also concluded that a floor with a mass greater than 200 kg/m2 acts satisfactorily in most cases. This possibly presents an issue since, at such masses, floors can’t be regarded as lightweight elements; bearing in mind that a dense concrete slab floor 150mm thick would be about 350kg/m2. This would be especially of concern for seismic considerations, where we may find that different bracing schemes are required. However, Sipari (2000) also suggested that lightweight floors full of mineral wool in the airspace could be developed to satisfy occupants, based on their results; it is not said how, ‘though. Sipari also produced a figure (reproduced in Figure 1-2) showing where timber floors perform poorly against concrete floors and in what frequency range certain resilient components in a floor improve performance. In the previous summaries no comment has been made of vibration damping. Work by Walk and Keller (2001) emphasised the importance of considering vibration damping in floor performance, since they believed that a lightweight floor will not have enough mass to perform well without extra damping.
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Impact Sound Pressure Level
Timber floor with ceiling Bare concrete floor
Problem range for lightweight floors
Resilient ceiling improvement range Floating floor improvement range Soft covering improvement range
16
32
63
125
250
500
1000
2000
4000
Frequency (Hz) Figure 1-2. Impact sound insulation of a timber floor compared to a concrete floor and areas where certain resilient aspects of the floor design will change its performance (after P. Sipari). The soft covering and floating floor improvement range can start at lower frequencies than shown; it depends on the type of system (e.g. heavy floating floor systems or carpet on underlay can show significant improvements starting at approximately 100Hz).
Existing High-Frequency Performance understanding. Although this project is focused on improving the low-frequency performance of timberframed floors, the high-frequency performance2 is a critical aspect of a floors performance too. It is often the case that if there are high-frequency problems, they overshadow low-frequency issues. Having said this, it is easier to deal with high-frequency than with low-frequency problems in lightweight floor systems. One of the reasons for this is that it is easier and more meaningful to measure and rate the high-frequency impact insulation performance of a floor using standard methods, and so it has been easier to develop solutions. In the case of lightweight timber floors, the issue of high-frequency impact (and airborne) insulation comes down to one of resilience and disconnection between masses:• To reduce high-frequency vibration being transmitted into the floor, the upper surface should be soft, or if hard, floating on a resilient layer. • For vibration that has entered the floor, to prevent it from being transmitted to the ceiling and then radiated into the space below the floor, there should be good decoupling of vibration to the ceiling by use of resilient ceiling connections or separate ceiling joists mounted on resilient supports. There should also be good airborne sound decoupling between the floor and the ceiling in the form of a cavity with fibrous infill. Guidance for reducing high-frequency impact sound transmission through lightweight floors is available in a number of text books on building acoustics. Recent work by Warnock and Birta (1998), where 190 floor systems were tested for sound insulation performance, did result in a number of observations for guidance on the matter of impact insulation of lightweight floor systems, as well as a empirical, regression-based formulation to predict the Impact Insulation Class3 of a floor system. 2
In the context of this research project high-frequency refers to frequencies above 200Hz, and low-frequency to those below 200Hz. Strictly speaking, you might regard the frequency range above 200Hz to be mid and high frequency realm. 3 Impact Insulation Class (or IIC) is defined in the ASTM set of standards. Page 17
As far as this project is concerned, we will only be concerned with keeping a weather eye on the high-frequency performance; in the sense of noting whether particular designs are better or worse for high-frequency impact sound insulation performance, as well as doing standard tapping machine tests on all floor systems. This analysis of existing knowledge is extended in Chapter 2; please refer to that chapter for more information. This section only covered the broad knowledge of floor design. Further research has been done into other aspects of the project such as the subjective analysis and the theoretical modelling. The summaries of the literature available for those aspects of the project are available in their associated chapters. 1.4
THE STRUCTURE OF THE RESEARCH PROJECT.
The research project was structured in order to respond to the factors influencing the problem of the low-frequency impact insulation of timber floors. With relatively minor attention being paid to the issue of the higher frequency impact insulation of timber floors. The project was divided into these three areas:1) Low-frequency theoretical modelling of timber floors and receiving rooms. 2) Experimental measurements of the impact insulation of floors for both low and high frequencies. 3) Subjective assessment of the floors. Obviously these areas are not independent of each other, and the results of one area influences the progress and decisions made in other areas. Theoretical modelling. Theoretical modelling is important to enable deeper understanding of what is happening and to enable predictions without having to build numerous floors to test to produce empirical results. It also enables the testing of ideal or extreme situations to illustrate concepts. In this project a low-frequency theoretical model of a joist floor was developed, as well as a lowfrequency model of a receiving room. Chapter 3 describes the development of both models. Once developed, tested against measurement, and refined, the theoretical modelling was used to perform a trend analysis on parameters of the floors. This trend analysis is presented in Chapter 4. Experimental measurements. A series of experimental floors were built in a laboratory and tested for both low and high frequency performance. The procedure used to test the low-frequency performance consisting of directly measuring the vibration of the floor using a shaker to excite the floor and a scanning laser vibrometer to measure the vibrations that resulted in the floor. Chapter 7 describes this procedure and contains a selection of the raw results. Standard tapping machine measurements were also made on the experimental floors; these results are contained in Chapter 8. Diagrams and photographs illustrating the design and construction of these floors are contained in Chapter 11. Subjective analysis. As mentioned before, a critical aspect of the impact insulation performance is how occupiers might react to the sounds of impacts on various floor designs. For this subjective aspect of the project, recordings of various types of impacts were made on the experimental floors, and played back to test subjects in a listening room. The feedback from these test subjects was then used to compare a selection of the experimental floors and to give
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information which would allow the generation of a suitable low-frequency assessment rating system for a floor. Chapter 6 describes the subjective analysis in detail. 1.5
CONCLUSIONS OF THE ANALYSES.
Theoretical Analysis Conclusions. In this section we offer some conclusions from the analysis of the theoretical model which is found in Chapter 4. These are divided into particular regions of the floor. The descriptions of the trends of the theoretical analysis relate to changes from a ‘basic’ intertenancy floor, illustrated in Figure 1-3. Flooring plywood or particleboard (floor upper)
300mm x 45mm (>12GPa) LVL Joists at 400mm – 450mm centres
300mm sound control fibreglass infill
RSIC-1 Resilient Clips Steel ceiling batten at 600mm centres 2
2 x 13-16mm plasterboard (25kg/m ) Figure 1-3. Illustration of the 'basic' inter-tenancy floor.
Joists. • • •
It would appear that massively increasing the stiffness of the joists substantially improves performance. However, at least a four-fold increase in bending stiffness of the joists from the ‘basic’ floor is required for a significant gain. Increasing the damping of the joists does improve results by reducing the resonance peaks, especially the fundamental. The addition of transverse stiffeners made from blocking and tie rods can show some improvement by increasing the spacing between resonances. The improvement is not very great however, especially for wider floors where much greater transverse stiffness is required to achieve significant results. Such a feature may be best used for very narrow floors.
Floor upper (section of floor on the joists). • •
It is no surprise that increasing the surface density of the floor upper does improve the performance, but after about 100kg/m2 it would appear that minimal gains are to be had, unless unreasonable surface densities are used. Increasing the bending stiffness of the upper only offers slight gains.
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•
Increasing the damping of the upper offers some significant gains in the performance in terms of reducing the resonance peaks. However, the performance as indicated by the loudness of the low-frequency impacts is limited by the first horizontal resonance in the room. In some cases, a resonance in the floor might coincide with that in the room, and in such cases damping would be obviously beneficial.
Floor cavity. •
•
The major conclusion from the floor cavity results is that for cavity depths greater than about 200mm the resilient rubber ceiling clips are the dominant sound transmission path. It is clear that very significant gains could be had by reducing the stiffness of the ceiling clips, or by using independent ceiling joists. However, independent ceiling joists can be prone to flanking transmission issues in a similar way to staggered stud walls. It is interesting to observe the effect increasing the damping of the ceiling clips has on performance. This appears to be due to the fact that, since the ceiling clips are a dominant transmission path, increasing the ceiling clip damping reduces the massspring-mass resonance of the floor system at around 30-40Hz. We also see an improvement in other low-frequency resonances.
Ceiling. •
•
Increasing the surface density of the ceiling improves the performance significantly. It would seem that, for a given amount of mass in the floor system, having about half the mass on the floor upper and half in the ceiling produces best results. This result relates well to the fact that airborne sound reduction in double-leafed constructions performs best for a given amount of mass when an equal amount of mass is to be found on each leaf. Greatly increasing the stiffness of the ceiling can have a detrimental effect whereas increasing the damping has a positive effect. Both of these results are probably related to the fact that the dominant sound path to the ceiling is through the ceiling clips.
Floor and room dimensions. •
• •
Increasing the span of the floor tends to improve performance up to a point. In part, this effect appears to be due to the movement of the fundamental resonance along the longest length of the room to a different frequency which might start to coincide with resonances in the floor. Changing the width of the floor does affect the results, but produces no trend as such, apart from increasing the size of the receiving room and hence the overall sound absorption. Changing the height of the receiving room only changes the results above the first vertical mode of the room (at around 60-80Hz, depending on the height). As a result, there is little influence on the loudness ratings, particularly for footstep sounds, since the energy is mostly concentrated below 80Hz.
Experimental Analysis Conclusions. In this section the conclusions from the experimental impact insulation results are presented. More detail can be found in Chapter 5. Low-frequency conclusions.
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The conclusions drawn from the low-frequency testing on the floors tend to be the same as those found in the theoretical model analysis, although what was experimentally tested was a subset of the analysis that could be done theoretically. In summary, the conclusions are:• The addition of transverse stiffeners did show the ability to reduce the density of resonance frequencies in the low frequency region. • The addition of mass and stiffness in the floor upper improves low-frequency performance. • The addition of damping in the floor upper improves low-frequency performance. • The use of a sand/sawdust mix as an infill in a battened cavity in the floor upper provides good results, by way of adding mass, adding a lot more damping, and adding some floor upper stiffness. • Extra ceiling layers improve low-frequency performance. • Independent ceiling joists can improve the low-frequency performance if care is taken to isolate them and the ceiling from vibration from the edge of the floor. This shows that the ceiling clips (even the rubber RSIC clips used) are the dominant sound transmission path. When care was not taken to isolate the ceiling joists and the ceiling, they performed as well as the RSIC clips. High-frequency conclusions. Although the focus of the project was not exactly on high frequency impact insulation, we did make standard tapping machine measurements on the floors and did find some interesting results:• The addition of transverse stiffeners in a floor significantly improved the highfrequency impact insulation (by 5dB in the floors tested) for the case when the floor upper was thin with little stiffness (e.g. one layer of plywood). • Extra ceiling layers did not improve the high-frequency impact insulation. • The span of the floor did not affect the high-frequency results. These are the more interesting conclusions from the high-frequency results, further conclusions are made in Chapter 1. Subjective Analysis Conclusions. In Chapter 6 the subjective analysis is described. A number of timber floor designs (nine in total) were subjectively tested using impacts that consisted of a standard Japanese impact ball, walking, and the tapping machine. These timber floors were compared against a reference 150mm concrete floor with an added suspended ceiling so that it met the Australian building code ( Ln,w + CI ≤ 62 ). One conclusion from the subjective analysis was that a floor design consisting of 85mm of sand in the floor upper, as shown in Figure 1-6, performed as well as the reference concrete floor for the low-frequency impacts (viz. the ball drop and the walking. Another conclusion was that the subjective results correlated well with loudness measures of the impact sounds, enabling such rating methods to be used for further analysis. Buildability Conclusions. Although there is not a separate chapter on conclusions to be had about buildability, it was a topic studied by asking Australian housing developers about such things. As a result of this discussion and through the existing knowledge of members and companies of the project team, some buildability issues did come out as being important and are listed:• The overall depth of the floor is an issue, however, the view was expressed that it is not a critical factor: designs can be adjusted to accommodate deeper floors, if necessary. In fact, it is good to have deeper joists (300mm) to accommodate air conditioning services, and to achieve greater spans. Page 21
• •
•
The total weight of a floor is an issue, for seismic concerns in New Zealand, but a weight of about 150kg/m2 is acceptable if standard LTF bracing systems and methods are to be used. The use of wet trades is an important factor. The delay and project management issues they bring to the job are very important. One major advantage of timber construction is that they lack wet trades in the construction. This would seem to rule out the use of concrete screeds. Cutting and laying of multiple layers of sheeting material is time consuming. To overcome this, the inter-tenancy floor for a whole tenancy could be completed and then infill walls added later.
Other Considerations. There are some other, miscellaneous considerations which are worth noting:• Another issue is concern about the embodied energy of a building. Timber is seen as a material with a low embodied energy (as well as being a carbon store), and other materials used should have similar qualities, including being available locally (to reduce transportation energy requirements). • It is important that the floor not have noticeable felt vibrations. It is often stated that this requirement is met by ensuring the fundamental frequency of the floor is above 8Hz. • It has been observed by a number of people that a floor which feels solid is good (e.g. Pitts (2000) ). People have a tendency to like concrete screeds on timber subfloors for this reason. Since subjective opinions are complicated, this could a contributing factor for reports that thick concrete screeds are effective. 1.6
SUCCESSFUL FLOOR DESIGNS.
The preceding analysis has led us to develop floor designs which are deemed to be successful in the eyes of the requirements of the brief. We therefore define a successful floor to be one which, according to subjective testing we have done, has similar performance to a 150mm concrete floor. We also require that the floor be buildable with skills that exist in the market, and that there be few proprietary products in the floor system. We also would like the floor to be a dry construction to retain one major advantage of LTF construction. Floor design A. The initial testing phase of the project and the theoretical modelling showed that a floor consisting of an upper with a deep layer of sand/sawdust mix could provide a solution. Subsequent subjective analysis showed it to be about as effective as a 150mm thick concrete floor. This tested solution design is shown in Figure 1-6. In the testing programme this floor was designated ‘Floor 9’. The standard tapping machine (ISO 140,717) results of this floor are Ln,w=48 dB, CI=-2 dB, CI,50-2500=9 dB. The cost of this floor has been estimated by a qualified quantity surveyor to be $A 63 more per m2 than the ‘Basic floor’ of Figure 1-3 for construction in Sydney or Melbourne (See Chapter 9 for more information about construction cost estimates. The depth of the floor is 504mm, and weighs 156 kg/m2 (113 kg/m2 for the floor upper, 25 kg/m2 for the ceiling). The joist span of this design tested was 5.5m which gave a fundamental resonance of 14.5Hz. Possible alterations to the shown floor design. To avoid felt vibration problems it is recommended that the fundamental frequency be above 8Hz. For vibration control, a span of 6.5m could therefore be attained with the joists
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used, subject to other structural considerations. The more rigorous analysis in this project may allow designers extra span depending on what limits have been applied in previous evaluations for span tables. A joist spacing of 400mm is shown; this could be changed to 450mm, without undue effects, since such a small overall change in stiffness has an insignificant effect on results. The floor is quite deep overall; however theoretical results do show that with the RSIC clips used, the cavity depth could be significantly less without much change to the results. The problem would be making the joists stiff enough to carry the weight. A possibility here is to reorient the battens so that they are parallel to and on top of the less deep joists, and screw the battens into the joists resulting in a composite action. The cavity is shown full of fibreglass infill of high flow-resistivity. Theoretical modelling has shown that with the use of RSIC clips, using less infill with less flow-resistivity makes little difference to the low-frequency performance. The ceiling is shown as being two layers of 13mm plasterboard. The critical aspect of the ceiling for low-frequency impact performance is that it has a surface density of 25 kg/m2; 2 layers of 16mm plasterboard with the same or greater overall surface density would be acceptable (if this were needed for fire performance). The ceiling battens don’t appear to be a critical element with the RSIC clips used; they could be replaced by different battens.
Figure 1-4. Design of floor tested in subjective testing and shown to have similar low-frequency performance to a 150mm concrete floor. (Known as Floor 9 in the experimental testing programme).
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Floor design B. The previous floor design (A) seemed to be an effective solution for producing a floor which is comparable to a concrete floor in performance, particularly for low-frequency performance. It does, however, use RSIC resilient clips to suspend the ceiling from the joists; whereas results from theoretical analyses did show that these clips are a major sound transmission path, even though the RSIC clips are very resilient when compared to other resilient clips or rails. There is opportunity to test a floor which uses independent ceiling joists to improve performance. However, as has been shown from experimental testing, such a system can be sensitive to how the ceiling joists are mounted, and how the ceiling edges are fixed. Nevertheless, assuming there is reasonable isolation from such flanking problems, if we use a ceiling supported by independent ceiling joists, we can expect better low-frequency performance from the ceiling system. If we use such a ceiling with independent ceiling joists, we can then reduce the amount of material used in the floor upper. We use the same principal of adding mass and damping to the floor upper by creating a cavity filled with sand and sawdust. However, with the added performance of the ceiling system we are able to reduce the size of the battens to 70mm and hence the nominal thickness of the sand/sawdust layer to be 65mm.This floor design (which is also known as Floor 25 in the test series) is shown in Figure 1-6. The independent ceiling joists used are made of LVL to prevent distortion of the ceiling from warping of timber; it would be possible to use I-beams instead. Steel ceiling battens are fixed to the underside of the independent ceiling joists to offer a cheap, easy and stable system to fix the ceiling to. In order to prevent flanking problems, the ceiling joist ends are supported on rubber vibration isolation pads, and the ends of the battens do not connect to the wall (a separation of 10mm is used).
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Figure 1-5. Design ‘B’ of floor tested and shown to have similar low-frequency performance to floor design A. (Known as Floor 25 in the experimental testing programme).
The low-frequency ceiling vibration measurements of the floor for the shaker excitation point at position ‘E’ are shown in Figure 1-6 with a comparison made against the results of floor design ‘A’ (a.k.a. Floor 9).We see from these results that the performance up to 100Hz is about the same as floor design ‘A’, with a bit more variation above 100Hz. The standard tapping machine (ISO 140,717) results of this floor are Ln,w=48 dB, CI=-2 dB, CI,50-2500=10 dB. From these two results we can conclude that floor design ‘B’ has similar performance to floor design ‘A’, and therefore also has similar performance to a 150mm concrete floor. The cost of this floor has been estimated by a qualified quantity surveyor to be $A61 more per m2 than the ‘Basic floor’ of Figure 1-3 for construction in Sydney or Melbourne (See Chapter 9 for more information about construction cost estimates. The depth of the floor is 484mm, and weighs 131 kg/m2 (90 kg/m2 for the floor upper, 25 kg/m2 for the ceiling). The joist span of this tested design was 5.5m which gave a fundamental resonance of 13Hz.
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Additional tapping machine tests were done on ceramic tiles adhered to a substrate of 10mm Gib gypsum fibreboard “Sound Barrier’, which was screwed to the floor. The results of this were Ln,w=53 dB, CI=-4 dB, CI,50-2500=3 dB. Possible alterations to the shown floor design. To avoid felt vibration problems it is recommended that the fundamental frequency be above 8Hz. For vibration control, a span of 6.0m could therefore be attained with the joists used, subject to other structural considerations. The more rigorous analysis in this project may allow designers extra span depending on what limits have been applied in previous evaluations for span tables. The ceiling is shown as being two layers of 13mm plasterboard. The critical aspect of the ceiling for low-frequency impact performance is that it has a surface density of 25 kg/m2; 2 layers of 16mm plasterboard with the same or greater overall surface density would be acceptable (if this were needed for fire performance). The ceiling battens don’t appear to be a critical element; they could be replaced by different battens.
2 √ ceiling, 3.2m wide Floor, Fin=1 N.
80 Basic Floor (#2) 85mm sand/sawdust (#9) 65mm sand/sawdust + independent ceil joists (#25)
√, dB (re: 5x10-8 m/s)
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Figure 1-6. Ceiling surface average velocity results for floor design ‘A’ (Floor 9) as compared to floor design ‘B’ (Floor 25). The results for the ‘basic floor’ (Floor 2) are also shown for comparison.
1.7
SUGGESTIONS FOR FURTHER WORK.
One of the side outputs of this project has been the theoretical model which was developed. As it stands it is in a form which is of use only to the researchers who developed it (due to the computer code it uses and its lack of an easy user interface). It is thought that this software could be useful to suitably interested and skilled people in industry. It could be adapted to make it more accessible to such people so that they can try out their own ideas and products (within the model’s limitations). Page 26
1.8
TECHNOLOGY TRANSFER OF OUTPUTS.
The primary channel for technology transfer and for getting systems through to the market is through our supporting companies. These companies are CSR, Winstone Wallboards, and CHH. The results will be presented to the above companies in a face-to-face presentation. This presentation will cover the construction details of the systems and the results together with all the features, benefits, strengths and weaknesses and the actions required of the product managers in order to exploit the best possible outcomes. The purpose of the face-to-face presentation is to impart the enthusiasm, passion and commitment of the research team to the product managers. This presentation will be made available on a CD or via the internet and will be given to the supporting companies involved in the research project. Technical support will be provided by a researcher who would provide ongoing technical input over a period of up to one year. This time period would facilitate the uptake of the technology by the various company product managers to enable successful penetration into the market. Queries about the details of the features and benefits can be answered quickly and directly by the people who undertook the research work. To ensure successful implementation and transfer of the technology, additional results, photographs, etc. will be provided, if required, as part of the ongoing technical support to product managers. The companies supporting the research project have a strong marketing capability and have been very successful in the promotion of new innovation and componentry in the field of noise control. Therefore, provided the presentation to the product managers of these respective companies is clear and timely and fills the marketing personnel with enthusiasm, then the implementation of this new technology should be carried out with due diligence and corresponding market growth. Communication of this new technology will utilise the existing marketing teams within the respective supporting companies, with support to the product managers and product development teams being sustained over a period of one year in order to clarify, confirm, expand and provide further details as and when required by the respective supporting companies. To communicate results to FWPRDC levy-payers and key stakeholders a document will be made available for distribution to these groups summarising the results, recommended designs and benefits, and possibly suggesting how timber producers may be able to take advantage of this information. Part of this communication can be a presentation to a meeting of the Timber Association Network in Sydney, as part of the technology transfer project on MRTFC run by the TDA.
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1.9
REFERENCES.
Blazier, W.E, DuPree, R. B. (1994). “Investigation of low-frequency footfall noise in woodframe, multifamily building construction”, The Journal of the Acoustical Society of America, 96(3), 521-1532 Hveem, S. (1998). “Comparison of low frequency impact sound insulation of different Nordic lightweight floor constructions”, Proceedings of Acoustic Performance of Medium-rise Timber Buildings, Dublin, Ireland, Dec. 1998. Pitts, G. (2000). Acoustic Performance of party floors and walls in timber framed buildings, TRADA Technology report 1/2000. Sipari, P. (2000). “Sound Insulation of Multi-Storey Houses – A Summary of Finnish Impact Sound Results”, Building Acoustics, 7(1), 15-30. Walk, M. & Keller, B. (2001). “Highly sound –insulating wooden floor system with granular filling”, Proceedings of ICA 2001. Warnock, A.C.C., Birta, J. A., (1998). “Summary report for consortium on fire resistance and sound insulation of floors: sound transmission class and impact insulation class results”, NRC-CNRC Report IRC-IR-766.
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2 OVERVIEW OF EXISTING FLOOR SYSTEM DESIGNS AND RECENT RESEARCH RESULTS. 2.1
INTRODUCTION.
The problem of low-frequency impact sound insulation in light-weight timber floors has been an issue for a long time. In recent years, research and anecdotal evidence have identified the problem as being of major concern for customers. In particular, the increased acceptance and use of light timber-framed construction in various parts of the world has highlighted the issues in certain countries (for example, in the US Blazier and DuPree (1994) highlighted increased customer perception of low-frequency impact sounds). As a result, a number of research projects have looked into this issue. Probably the most significant research project into this area was done in Scandinavia, by Finland, Sweden, Norway and Denmark. As part of the socalled Nordic R&D project “Multistorey timber frame buildings”, the project consisted of each contributing country selecting a number of suitable floors (after some experimental development), and then installing these floors into real building developments with occupants. This project spanned 5 years and finished in 1999. A number of summary papers have been completed by the main researchers into this project, a good one being that produced by Hveem (1998), the principal researcher of this project. 2.2
EXISTING LOW-FREQUENCY PERFORMANCE UNDERSTANDING.
The results of the Nordic R&D project resulted in a number of conclusions and desires for further work. It is worth summarising their conclusions here, because they seem to be a set of effective conclusions about the problem – echoing conclusions of other research projects. Hveem (1998) produced these conclusions:• There is trend against stiffer joist construction in the form of deeper joists, i.e. the fundamental frequency shouldn’t be too high. This echoed by Blazier and DuPree (1994). • Lightweight floating floor systems (e.g. a couple of layers of particleboard on 20mm mineral wood board) don’t improve impact insulation below 160Hz. Even heavyweight floating floor systems (e.g. 50mm dense concrete on 20mm mineral wool board) won’t improve low-frequency performance below 50Hz, at best. • The elastic suspended ceiling systems they used perform well, but have a resonance frequency of about 30Hz, and hence have limitations. • Completely filling (or, even overfilling) the cavity with mineral wool has a positive effect on performance, especially for the cavity depths found in floors. • For the low-frequency range it is important to separate the most dominating natural frequencies in the floor system from the modes in the room, given by typical dimensions. • The peak energy of a footfall occurs in the frequencies below 50Hz. Sipari (2000), the leader of the Finnish contribution to the acoustic aspect of the Nordic R&D project, concluded that the way forward is to increase mass and stiffness of the floor and floor parts. They found in their testing that a composite floor consisting of concrete slab bound to joists, so that they structurally work together, is an effective solution. They also concluded that a floor with a mass greater than 200 kg/m2 acts satisfactorily in most cases. This possibly presents an issue since, at such masses, floors can’t be regarded as lightweight elements; bearing in mind that a dense concrete slab floor 150mm thick would be about 350kg/m2. This would be especially of concern for seismic considerations, where we may find that different Page 29
Impact Sound Pressure Level
and additional bracing schemes are required. However, Sipari (2000) also suggested that lightweight floors full of mineral wool in the airspace could be developed to satisfy occupants, based on their results; it is not said how, ‘though. Sipari also produced a figure (reproduced in Figure 1-2) showing where timber floors perform poorly against concrete floors and in what frequency range certain resilient components in a floor improve performance. In the previous summaries no comment has been made of vibration damping. Work by Walk and Keller (2001) emphasised the importance of considering vibration damping in floor performance, since they believed that a lightweight floor will not have enough mass to perform well without extra damping. It is worth noting that in some parts of Europe it is believed that there are two ways to obtain good impact insulation performance in floors: either through the use of mass in massive construction, or through the use of separation between the floor and ceiling for lighter constructions. Some are so convinced of the latter that they have regulated that a lightweight floor system must be at least 500mm deep4 in building codes.
Timber floor with ceiling Bare concrete floor
Problem range for lightweight floors
Resilient ceiling improvement range Floating floor improvement range Soft covering improvement range
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Frequenc y (Hz ) Figure 2-1. Impact sound insulation of a timber floor compared to a concrete floor (after P. Sipari).
2.3
EXISTING HIGH-FREQUENCY PERFORMANCE UNDERSTANDING.
Although this project is focused on improving the low-frequency performance of timberframed floors, the high-frequency performance5 is a critical aspect of a floor’s performance too. It is often the case that if there are high-frequency problems, they overshadow lowfrequency issues. Having said this, it is easier to deal with high-frequency problems than with low-frequency problems in lightweight floor systems. One of the reasons for this is that it is easier and more meaningful to measure and rate the high-frequency impact insulation performance of a floor using standard methods, and so it has been easier to develop solutions.
4
This was communicated to the author by Jens Rindel of DTU, Denmark. In the context of this research project high-frequency refers to frequencies above 200Hz, and low-frequency to those below 200Hz. Strictly speaking, you might regard the frequency range above 200Hz to be mid and high frequency realm. 5
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In the case of lightweight timber floors, the issue of high-frequency impact (and airborne) insulation comes down to one of resilience and disconnection between layers of appropriate mass:• To reduce high-frequency vibration being transmitted into the floor, the upper surface should be soft, or if hard, floating on a resilient layer. • For vibration that has entered the floor, to prevent it from being transmitted to the ceiling and then radiated into the space below the floor, there should be good decoupling of vibration to the ceiling by use of resilient ceiling connections or separate ceiling joists mounted on resilient supports. There should also be good airborne sound decoupling between the floor and the ceiling in the form of a cavity with fibrous infill. Guidance for reducing high-frequency impact sound transmission through lightweight floors is available in a number of text books on building acoustics. Recent work by Warnock and Birta (1998), where 190 floor systems were tested for sound insulation performance, did result in a number of observations for guidance on the matter of impact insulation of lightweight floor systems, as well as a empirical, regression-based formulation to predict the Impact Insulation Class6 of a floor system. As far as this project is concerned, we will only be concerned with keeping a weather eye on the high-frequency performance; in the sense of noting whether particular designs are better or worse for high-frequency impact sound insulation performance, as well as doing standard tapping machine tests on all floor systems.
2.4
EXISTING LIGHTWEIGHT FLOOR COMPONENTS IN USE AROUND THE WORLD.
Having presented a brief summary of research into the testing and design of lightweight floor systems for the improvement of impact insulation, we can now look at features of lightweight floor design which are used around the world. The particular features will be examined separately with examples of their use. Layered upper surface floor systems. These systems consist of increasing the mass in upper part of the floor by adding layers of sheet material on to the base floor. They may or may not be placed on a resilient underlay to form a floating floor. In some cases the friction or air pumping that occurs between the layers provides extra damping. Examples of the materials used are flooring grade plasterboard (made from alphagypsum), extra layers of particleboard or plywood (or similar), fibre cement sheet and gypsum fibreboard. These systems are in common use around the world where lightweight constructions are used. For example, in Scandinavia these systems, consisting of chipboard/plasterboard/chipboard layers, were common from 1987 (Hveem, 1998). They also are used in Japan, and a version consisting of two layers of gypsum fibreboard on top of the subfloor is currently promoted by USG and Winstone Wallboards in Australasia. An example of this type of system is shown in Figure 2-2. This particular system happens to be a floating system.
6
Impact Insulation Class (or IIC) is defined in the ASTM set of standards. Page 31
Glass wool slab 19mm plasterboard
Figure 2-2. Floor design showing layered sheet material system (floating on glass wool). Also shows independent ceiling joists. (From TRADA Technology report 1/2000).
Concrete flags. In another attempt to add mass to the upper part of the floor, flags of concrete have been tried, ultimately covered with a wearing (and levelling) layer of sheet material. The flags have to be spaced by a few millimetres to prevent grinding together in service. This can be good way to get dense mass into the floor, without sacrificing dry construction advantages. These flags can be placed directly on the sub floor or floated on a resilient layer. Screed toppings. These systems consist of some sort of concrete poured onto the subfloor. They have the advantage that they can be self levelling, and hence are also used to level the floor. They also can take heating wires for a heated floor. The screed can be poured on a resilient underlay to form a floating floor. A common form of screed is a gypsum-based concrete, which sets quickly (in a matter of hours), allowing further building work to proceed quickly. Such gypsum concrete screeds are common in North America to the point of being almost standard practise. Gypsum concrete screeds have been trialled in parts of Europe in a floating configuration to positive effect. One trial was part of the Swedish aspect of the Nordic R&D project mentioned before and concluded that installed in a real building it proved to be more effective than layered systems in terms of occupier opinions, although lab test results may have showed the two types of systems to be have similar performance. It also has been observed by TRADA tests that the resulting surface feels good to people when they walk on it: it feels ‘solid’.
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One negative side to concrete screeds is the fact that they can take some time to dry properly, even if they can set quickly. 38mm of gypsum-concrete screed can take more than 2 weeks to dry out, even in warm and well ventilated conditions. This water retention problem has resulted in occasional timber rotting issues in North America. Another negative aspect to concrete screeds is that the hard surface they present can compromise high frequency impact insulation, and so a resilient underlay is often necessary for hard, wearing surfaces. A third issue for gypsum concrete is the fact that it has to be poured quickly using specialist equipment and labour. It appears to be a specialist trade in its own right. Composite acting floor systems. Some floor systems have an upper surface layer usually made of concrete which is directly bonded to the joists so that the upper surface and joists act together to increase stiffness. An example of this type of system has been produced by a company from Finland, Sepa Oy (Karjalainen, 2003). Figure 2-3 illustrates this particular floor design.
Figure 2-3. Composite wood-concrete floor system developed by Sepa Oy, Finland. Truss joists are used with the top nail plates protruding above the joist. A reinforced concrete layer is then poured over the floor. The concrete then bonds to the joists through the protruding nail plates.
Floating floor systems. In order to improve higher-frequency sound insulation, it is common to float the upper floor layer or layers on a resilient material. Usually this is only effective in reducing impact sound above 150Hz. An example of this was shown in Figure 2-2. Another common method of floating floors is to use battens which have a resilient pad on one side. There is a variant on the floating floor scheme where the subfloor has perforations in it to reduce the air stiffness in the resilient layer between the subfloor and the upper layer. An example of battens with perforations in the subfloor is shown in Figure 2-4. A problem with floating floor systems is that, in order to make then most effective, the edges must also be resiliently separated. It would appear that this can be difficult to implement consistently in practise.
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Batten with resilient pad.
Figure 2-4. Floor system showing floating floor consisting of battens with resilient pads on one side. Also note perforations in subfloor to reduce air stiffness in floating cavity. (From TRADA Technology report 1/2000).
Resilient or disconnected ceiling systems. A lot of vibration is transmitted through the joists to the ceiling. It is better that this be isolated in some way. A common method is to use a resilient rail or channel which spans across the joists and to which the ceiling is screwed. This idea is improved by the use of rubber (or similar) ceiling batten clips which are screwed to the underside of the joists, and to which the ceiling battens are clipped. Another method to isolate the ceiling from the rest of the floor, seemingly more common in Britain, is to use separate ceiling joists to which the ceiling is screwed (as shown in Figure 2-5). Another high-technology possibility and area of research is in the use of active noise control to control low-frequency sound for very light weight structures. Progress in this area continues, and for our problem a likely place for active noise control actuators is in the ceiling connections, where the stiffness of the air is overcome by ceiling clips with negative stiffness. An example of this sort of work is provided by Akishita et.al. (2004).
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Figure 2-5. Illustration of floor with separate ceiling joists. (From TRADA Technology report 1/2000).
Raised Floor systems. Raised floor systems (access floor systems) are like those found in computer rooms and offices where there is a lot of cabling to run under the floor. They are not that commonly used around the world for floors in apartments. They are however not unusual in some parts of Japan for fitting out concrete apartments. In that situation, their main application appears to be for levelling the floor. It was noted in Japan that the opinion of occupants is that these systems increase impact noise problems of the floors, due to resonances in the air cavity (Ueda and Kakehashi, 2004). Solid and semi-solid timber floor systems. Solid timber floors are occasionally seen in use around the world. Although it would seem to be an expensive use of timber, low-quality timber may have an application here. Recently the Swedish company Södra promoted mechanically laminated timber slab floors (from 70mm to 220mm thick) for use in multi-residential construction. It is possible that such a system could perform well in the low-frequency regime, if it were thick enough. Södra also produced a ‘semi-solid’ floor system made from joists spaced at 100mm centres, with the gaps filled with fibreglass. This presumably gives good stiffness (and mass) while providing a deep cavity for sound isolation to the ceiling. Such systems, however, are only worthwhile if factory made, and are probably beyond our consideration. Granular infills. Granular or particle-type materials have been used quite frequently in the past as an infill in timber structures. It was not uncommon to have sand or fly ash in timber floors in parts of the United Kingdom many years ago – the fill would be either placed on shelves between the joists or on the ceiling (which was made of material which could support the weight). The primary function of this fill was for sound insulation purposes. Another example of this is found in some old multi-storey timber buildings in New Zealand (e.g. the old parliament buildings in Page 35
Wellington), where volcanic scoria was used in the floors. More modern references to this are found in Switzerland, where sand has been used as a layer in both retrofit and new buildings (Lappert & Geinoz, 1998). Incidentally, Lappert and Geinoz do note that the sand should be heated to ensure no living things are introduced. Walk and Keller (2001) did recent work to develop a floor using a massive amount of ‘granular’ material on which a walking surface was floating. They do not say what exactly this granular material was and further communication with the authors did not reveal it, although they did say that it was being installed in a block of apartments. However, they said that the main reason for using this granular material was to take advantage of the high damping afforded by the granular material due to the friction between particles, because a lightweight floor, in their opinion, could never have enough mass to provide excellent sound insulation. Figure 2-6 illustrates this floor and shows how much granular filling there was in the floor (i.e. lots).
Floor walking surface
Floor lower surface
Granular filling
Figure 2-6. Swiss trial timber floor with upper floor surface floating on granular material (Walk and Keller, 2001).
Since granular materials, particularly sand, have been used with some success in buildings as a way of improving vibration damping, it is worth overviewing some of the literature which exists about this. It is clear from the literature that the damping processes which occur in granular materials are complicated and not very well understood apart form some specific instances. A good account of the use of sand with other mixtures of materials has been provided by Kuhl and Kaiser (1962) for use with concrete structures. They tested various sands and mixtures (fine sand, course sand, brick rubble, and mixtures of sand and sawdust), and found that hard granular materials with sharp edges or with a soft material (e.g. sawdust or rubber dust) gave better damping at lower frequencies. They thought that this was due to the sharp edges giving more friction with vibrational strains and the lower wavespeed of vibrations in the sand sawdust or rubber dust mixtures. The sand/sawdust mixture tested was 80/20 sand/sawdust. They also note that the impedance of the granular fill should try to match the impedance of the surrounding, structural material to enable maximum coupling of energy into the granular fill. They determined that the maximum damping was attained at cavity resonances in the granular fill. The damping was also found to be non-linear in the sense that it depended on amplitude of the vibrations: higher amplitudes result in more movement of the granules and hence more friction. Richards and Lenzi (1984) did measurements on the vibration damping due to sand and found that below a strain of 10-6 the particle movement is small and the damping in the sand is small and is probably not due to the friction of the particles; above that point damping becomes increasingly significant. They also noted that loose sand in cavities is useful because there is the added damping benefit of having the granules move around from regions of high density to
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regions of lower density. This movement is a maximum in resonances in the cavities which contain the granular fill. Xu et al. (2005) note that shear friction is the major contributing factor to the damping due to granular fills. Since our concern in low-frequency floor vibrations is the bending waves in the floor which would cause a lot of shearing of any infill, this is an important point to note. Sun et al. (1986) observed from experiment that, when looking at sand laid on a vibrating metal plate, the vibrational damping in the plate is a maximum at frequencies above when the thickness of the sand is about equal to 0.05λc, where λc is the longitudinal wavelength of the vibrations in the sand ( λc = c f , where c is the propagation speed of the vibrations (100 to 200 m/s for sand) and f is the frequency). Below this point there is a sharp drop in damping, and above this point there is a gradual decrease (due to the increasing weight of the sand packing down the sand below and stopping movement of the sand granules). Interestingly, sawdust is often mixed with sand when used for anechoic terminations for experiments with vibrations in beams. The sawdust is included to keep the sand from packing down, thereby improving its absorption characteristics. Other damping materials. If vibration damping is important, another way to include this is to add a constrained viscous damping material, for example like a viscoelastic polymer glued between plywood layers. This can be expensive, and the polymer’s damping performance can be dependent on frequency and temperature, but it is usually not dependent on vibration amplitude. Yet another way to achieve more damping is to have layers of material and to rely on the interaction between these layers to provide more damping, whether by friction between the layers, air pumping, or fretting (where the surfaces become damaged due to rubbing forming fragments thus contributing to frictional effects). 2.5
REFERENCES.
Akishita, S., Mitani, A, and Takanashi, H. (2004). “Active Modular Panel Systems for Insulating Floor Impulse Noise”, Proceedings of ICA 2004. Blazier, W.E, DuPree, R. B. (1994). “Investigation of low-frequency footfall noise in woodframe, multifamily building construction”, The Journal of the Acoustical Society of America, 96(3), 521-1532 Hveem, S. (1998). “Comparison of low frequency impact sound insulation of different Nordic lightweight floor constructions”, Proceedings of Acoustic Performance of Medium-rise Timber Buildings, Dublin, Ireland, Dec. 1998. Karjalainen, M. (2003). “Sound insulation in Finnish multi-storey timber apartment buildings on the basis of a survey of residents”, Proceedings Wespac 8, Melbourne. Kuhl, W., Kaiser, H. (1962). “Absorption of structure-borne sound in building materials without and with sand-filled cavities”, Acustica, 2, 179-188. Lappert, A., Geinoz, D.,(1998). “Experience in Multi-storey timber buildings consulting and field measurement”, Proceedings of Acoustic Performance of Medium-rise Timber Buildings, Dublin, Ireland, Dec. 1998. Pitts, G. (2000). Acoustic Performance of party floors and walls in timber framed buildings, TRADA Technology report 1/2000. Richards, E. J., Lenzi, A. (1983). “On the prediction of impact noise, VII: The structural damping of machinery”, Journal of Sound and Vibration, 97(4), 549-586.
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Sipari, P. (2000). “Sound Insulation of Multi-Storey Houses – A Summary of Finnish Impact Sound Results”, Building Acoustics, 7(1), 15-30. Sun, J.C., Sun, H.B., Chow, L.C., Richards, E.J. (1986). “Predictions of total loss factors of structures, part II: Loss factors of sand-filled structure”, Journal of Sound and Vibration, 104(2), 243-257. Ueda, Y. and Kakehashi, T. (2004). “A study on the relationship between bending vibration of access floor panel and floor impact sound level in an apartment building”, Proceedings of ICA 2004. Walk, M. & Keller, B. (2001). “Highly sound –insulating wooden floor system with granular filling”, Proceedings of ICA 2001. Warnock, A.C.C., Birta, J. A., (1998). “Summary report for consortium on fire resistance and sound insulation of floors: sound transmission class and impact insulation class results”, NRC-CNRC Report IRC-IR-766.
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3 THEORETICAL MODELLING OF A JOIST FLOOR. This chapter presents a mathematical modelling of lightweight timber-based floor structures. The joist floors studied here consist of two basic components, floor upper surface, ceiling and joists. The configuration of the model is progressively made complex by adding more components in order to approximate the real structure as closely as possible. The resulting solution formulae are written into computer codes, which compute the dynamics of the structure under a given force. This chapter is divided into three parts. The first part reviews the existing modelling methods of the LTF structures. Various articles are briefly reviewed and interrelated to each other. The second part gives the details of the floor modelling procedure, such as the Fourier expansion, composite of many components, interaction force by slippage. The third part outlines the model used to predict the sound transmission into the receiving room.
3.1
INTRODUCTION
In this chapter, we study vibration of a floor structure that has three basic components, upper plate, joist beams and ceiling. We use a mathematical modelling technique to study the dynamics of the structures. The term 'mathematical modelling' is here used for the model of the structure (LTF floor system here) using explicit formulae based on the individual material properties. In contrast, the implicit modelling uses the parameters that are derived from either the group of the structure or the whole structure. Each modelling has its advantages and disadvantages. In recent years there have been numerous theoretical studies on the vibrations of walls, floors and ceilings, because these building components are the primary source of sounds in a room. A difficulty arises from the fact that these building components themselves are made up of many components with widely varying mechanical properties. Furthermore, the connections between different components have not been studied in detail. There are various ways to connect the floor to the joists. We here consider simple spring model the resistance when there is slippage between the components. The amount of the resistance at the connection can be changed by varying the spring constants. We here show how the Fourier expansion method can be applied to fairly complex structures. The resulting solution is computationally efficient and robust for a wide range of physical parameters. In part II of this chapter, we will derive the differential equations that describe the upper plate and the joist beams as Kirchhof plate and Euler beams. In part I of this chapter, various articles concerning the dynamics of the composite structures, which form a part of LTF floor system. The articles are reviewed according to their time of publication, authors and the solution techniques. The relationship between the articles is also considered. Over the course of the project the theoretical model of the floor system was developed and refined using the experimental results from the mock-up floor structure. During the course of the research, it has been found that the interaction between the upper plat and the joist beams is crucial in determining the frequency response of the structure. The model initially had the upper plate and the joist beams. It was then made progressively complex to follow the experimental mock-up floor in realty. Eventually the model consists of the upper plate, joist Page 39
beams (for the upper plate and the ceiling), cavity air, and the sound damping filling in the cavity (glass fibre wool). 3.2
PART I: REVIEW OF EXISTING MODELS
This section introduces the papers of importance regarding theoretical modelling of wood floors. The papers are interrelated to each other. Figure 1 shows how the articles by the various researchers are related to each other. From that relationship, we may categorize the papers into three groups (Groups (a), (b) and (c)), of which two can be categorized as deterministic models and the other as empirical models. The rule of the abbreviation is that the first two letters of the author(s) and the year of the publication are used. For example, the paper by Langley and Heron in 1990 is written as LaHe90. Additional a, b,… are used when there are more than one paper by the same author(s) in the same year. For example, Ma80a, Ma80b and Ma80c are the papers by Mace in 1980, in the order listed in References here. The most commonly used text books in all papers are Morse68, Cremer73 and Fahy85. The series of technical reports by Hammer and Brunskog Hammer96 and Brunskog02 give detailed studies of the modelling of tapping machines and floor vibration. Their technique is based on the series of papers by Mace, Mace80, Mace80b, Mace80c, which deals with a periodically stiffened elastic plate. Mace's method is based on Mead71, Evseev73, Lin77 and Rumerman75. A few researchers in Japan have been studying the double leaf wall structure using the combination of the above two techniques, Yairi02 and Takahashi83. In another Group of papers that deal with the transmission of vibration across a plate-beam joint, Langley90, Craik96, Craik00 are discussed. Their method is based on the techniques that are developed for laminated plates in Ashton70. The equation of motion and the force (moment) equilibrium relationship for laminated plates are derived in Ashton70. In Langley97 and Craik00a, the transmission and coupling loss factor are used in SEA to find sound transmission through a double-leaf structured walls with various connecting methods. In Group (c), an example of an orthotropic model by Emms Emms02, Emms04 is given. The paper by Blazier and DuPree Blazier94 uses a homogeneous plate model, which uses a constant factor to convert the vibration velocity to sound pressure. The stiffness of the plate is then calculated using a generic formula based on the static elastic modulus of the individual components of the floor. For example, the physical parameters and formulae that are necessary to compute the total stiffness can be found in Australian Standards Australia93 in Appendix D.
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Figure 3-1: Diagram depicting the relationship between the paper.
In the following subsections, the articles by Brunskog, Craik and Emms, one from each Group in figure 3-1, will be discussed in detail because each of them represents its group well. On the left hand side of the dashed line are the deterministic models that derive explicit or approximate formulae for the deformation of the structure. On the other side are the empirical models that derive the sound pressure generated by the structure by assuming the structure is either homogeneous or orthotropic elastic plate. We however will not discuss the articles
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concerning SEA in Group (c). The same notations that are used in the original papers are used when there is no confusion. Each subsection should be regarded independent from others. Group (a)
Figure 3-2: group of articles in (a) and brief explanations of them.
Figure 2 shows the papers in Group (a) and short comments describing them. We here mainly discuss the model used by Brunskog Brunskog02, in which a localized time harmonic force is applied on the infinite floor surface. The forcing function is given by F ( x , y , t ) = δ ( x − x 0 , y ) e i ωt where δ(x-x0,y) is Dirac's delta function. The term exp(iωt} will be omitted since every term is time harmonic. The floor and the ceiling are joined by periodically placed parallel joists (beams). Note that the system is shift invariant in the y-direction, thus the forcing is placed at y=0 (see figure 3-3).
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Figure 3-3: Schematic drawing of the model used in Brunskog02.
In Brunskog02, thin plate equations coupled with forces from the air between the plates and the supporting beams (Euler beams)
(3-1) where pa and pb are the pressure due to the air and the beams between the plates and
The flexural rigidity of the plate is computed by
where h and ν are the thickness of the plate and Poisson's ratio, respectively. In the thin plate theory the thickness h is smaller than other physical dimensions of the plate, such as the spanwise size of the plate and wave length. Equations (3-1) are equilibrium relationship of the forces in the plates. ∆2-term (bi-harmonic) and m-term represent the bending and kinetic energy. The external force maybe generated using a tapping machine or human feet, but we do not consider how the force is generated here. When the thin plate theory is used, all displacement components (in-plane and transverse) of the plate surface can be expressed using the vertical displacement of the neutral plane. A supporting beam is modelled as an Euler beam, which is represented by the following equation
where E, I and σ are the Young's modulus, moment of inertia and the mass density of the beam, respectively. Euler beam is a 1 dimensional version of the thin plate theory, that is, only the bending deformation is taken into account. For an Euler beam I=bh3/12, where b and h are beam's width and thickness, respectively. There are six unknowns in the system of equations, w1, w2, pc, pb1 and pb2. These quantities are related to each other by the following continuity conditions,
(3-2) Page 43
These conditions describe that the beams (joists) and the floor boards are perfectly joined without a gap at all time. However, each component is free to slip as it deforms. The system of equations is solved using the Fourier transform method, in the (x,y)-plane and on the y-axis at x=nl. The Fourier transform of function w(x,y) in the (x,y)-plane is defined as
The inverse Fourier transform is then defined as
The Fourier transform of equations (3-1) in the (x,y)-plane are
(3-3) The Fourier transform of on the y-axis is (3-4) The Fourier transform of equation (3-2) can be written as
Note that we used equation (3-4) and n'th supporting beam always remain on the plane, x=nl. Furthermore, the shear deformation of the beam and the moment acting on the plate result of the shear deformation are excluded from the model. The system of equation is solved using Poisson's summation theorem,
(3-5) where ŵ denotes the 1 dimensional Fourier transform of w on the y-axis. Because of the above relationship, it is possible to express the transfer function in terms of the summation over the transfer function at α=2π n/l. The pressure from the air in the cavity can be obtained by solving Helmholtz's equation for the air pressure p(x,y,z), (3-6) with the boundary conditions
Equation (3-6) is then solved using the Fourier transform in the frequency domain.
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The pressure from the air outside of the floor system is taken into account in Brunskog02. However, this is omitted here, since the method of solution is the same whether or not the air pressure outside is included. The techniques in Brunskog02, Yairi02 and Takahashi83 show that any forces (or moments) that can be expressed by linear combinations of w1 and w2 can be included in the right hand side of the plate equations (3-1). The equations then can be solved using the same methods given in Brunskog02 and Takahashi83. Furthermore, any linear combinations of the partial derivatives of w1 and w2 can also be incorporated in the model. The model described in this section omits the fact that the floor boards are normally nailed or screwed to the joists. Thus, the movement of the joists and the floor is restricted in some degree. Furthermore, deformation of the floor in the x direction is likely to be influenced by the shear deformation of the joists. Group (b) Craik and Smith Craik00 gives detailed studies of the mechanical conditions for double-leaf walls and their frames as a sequel to their preceding paper Craik00a. In Craik00 the transmission and the reflection of plane waves at the plate-beam (plate-plate) junction is derived from the model explained in Langley90. The transmission is then used in SEA model for the whole wall structure. The wall consists of two plates and frames that connect them. In that regard Craik00 should perhaps be categorized in Group (c). However, we put the paper in Group (b) because it mainly describes the mechanical properties of the platebeam (or plate) junction. The frames are modelled as either beams or plates. Figure 3-4 gives brief descriptions of the papers in Group (b) and Group (c). The plate-plate junctions are decomposed into 5 components as shown in figure 3-5. Figure 3-5 shows that all the forces and moments within linear solid mechanics are taken into account to the model. Note that plates 1-4 are semi-infinite, which is different from the model in section 2.1.
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Figure 3-4: The articles in the groups (b) and (c), and brief explanations of them.
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Figure 3-5: Coordinate system, forces and moment acting on each component of the plate-beam junction (copied from Craik00).
In Craik00, it is concluded that the plate-plate junction model performs better than plate-beam model for low-frequency sound. It is not yet confirmed whether or not this is true for wood floors. Plate 1 is excited by a plane wave of frequency ω that is incident from x=-∞ to the junction, then propagates into the rest of the structure. Each plate, for example plate 2, is represented by three displacement components ς2 (longitudal direction), ζ2 (longitudal direction orthogonal to ς) and η2 (transverse direction). Thus, there are five sets of these displacement components for the whole structure. The equations of motion are
where ξ and ς are the in-plane displacement and η is the transverse displacement. Note that, there are five plates (see figure 3-5), thus there are five sets of the displacement components.
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In contrast to the model in the previous section, the plates here are described using all three independent components of the deformation. When the plate is excited by a single frequency plane wave incident to the junction at an angle θ, the time and y dependence in the above equations can be taken away. It is also possible to express the waves in each plate by modal expansion. For example plate 1 is expressed by
where the bending, longitudal and transverse wave numbers (spatial frequency) are
Note that TT0, TL0 and TB0 are the amplitudes of the incident waves in the two in-plane and transverse (bending waves) directions. The other amplitudes (denoted by T with a subscript) are the unknown amplitudes to be determined. There are oscillatory and exponentially decaying modes in transverse displacement, but only oscillatory modes in the in-plane components. In plates 2 ~ 4, there only the modes that propagate away from the junction I (II). Thus only two modes are needed for the displacement components in plates 2 ~ 4. The waves travel back and forth between junctions I and II as some energy transmits and some is reflected at the junctions. The displacement components in plate 5 are
where (+) refers to the amplitude of waves travelling from junction I to junction II, (-) refers to the amplitude of waves travelling from junction II to junction I. The boundary conditions are
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Similarly for the junction II, we have
The conditions at the junction are then used to determine the coefficients of the modes. The conditions are derived from the equilibrium of the forces and moment. There are 24 unknowns and the same number of equations. In Craik00, the beam is assumed to be either screwed at points or perfectly glued. In the future we may consider modifying the conditions to accommodate some freedom of movement at the contact surface since the floor boards are not normally completely glue to the joists. In Craik00, it is argued that frame (joists) should be modelled as a plate rather than as a 1 dimensional beam in a low-frequency range. It remains to be seen whether or not an infinite number of periodically placed joists can be modelled (and solved) using the method described in this subsection. Group (c) In Emms04, a variational method for an orthotropic plate to find the vertical displacement of the plate that minimizes the total energy in the plate. An orthotropic plate has a constant stiffness in one direction. The total energy in a time interval [0,t1] is expressed as
where L is the Lagrangian of the plate. The formula for L can be found in any of Morse68, Cremer73 and Fahy85. The solution w minimizes H, i.e., the first variation is zero, The solution to the above variational equation can be found numerically using Rayleigh-Ritz method as shown in Emms04. Sound radiation from a vibrating plate (flat surface at z=0) can be expressed by the following integral over the floor surface
where ρ is the mass density of the air in the room. G denotes Green's function satisfying Neumann condition
The walls and the floor of the receiving room are assumed to be acoustically rigid. Emms Emms04 states that his model does not perform well in the high-frequency range. The model in Blazier94 predicted ISPL using the formula where V and ft are the maximum velocity of the floor and the transfer function of the floor in dB, respectively.
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The total stiffness of the floor structure is calculated using the stiffness of the individual parts and the joint conditions between the plates and the joists from Australian Standard Australia93. It should be noted that the physical parameters used in this model are measured under static forcing on the material. Thus, it is uncertain whether or not those parameters are valid for vibrating structures (with varying frequency). Concluding remarks Each of the models introduced here has its strengths and weaknesses. The models in Group (a) give explicit formulae and deformation of the floor everywhere. However, the interaction at the plate-beam junction is overly simplified to exclude any forces acting on the contact surface between the plates and the beams. The models in Group (b) takes into account forces and moment acting on the contacting surface. However, the interaction between the joists is not taken into account. The models in Group (c) can predict the ISPL using the simple formula with the physical parameters of the individual components of the floor. However, the parameters are measured for static load and the model has been shown to be inadequate in predicting the dynamics of the structures. It is not possible to make a definite statement how well the models shown here predict the performance of real floor structures. Each model lacks some important features of the floor when it is vibrating at a low frequency. There are no standard guidelines how to assess the theoretical models. In order to determine the physical properties of the floor structure, we need to know the details of interaction at plate-joists-plate junctions. Our next step is to compare the models in group (a) with experimental data taken from our own mock-up floor in Tamaki. In the following sections (part II of this chapter), we present our own modelling effort with some comparison between the theory and the experiments. 3.3
PART II: OUR MODELLING FOR LTF FLOOR SYSTEMS
We detail our modelling of the floor/ceiling system in this section. We start with the simplest floor configuration, which consists of the upper plate and the joist beams. The model will then be made more complex to approximate the real experimental structure. The detailed comparison between the theoretical results and the experimental data will be presented in the later chapter. A brief description of the computer codes will also be given at the end of the section. Solution of a simple joist floor 5.5 m
Plywood
15 mm
300 mm
3.2 m
400 mm
45 mm
Figure 3-6: Schematic drawing of the experimental mock-up floor.
We consider a joist floor that is spanning over [0,A] and [0,B] in the x and the y directions, respectively. The z-axis points downward. The thickness of the upper plate and the depth of the
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joist are h0 and h1, respectively. The cross-section of the structure is shown in figure 3-6. The upper plate is modelled as a Kirchhof plate and the beams are modelled as Euler beams. Equations for the upper plate and the joist beams The upper plate is here excited by the time-harmonic forcing with radial frequency ω. The vertical displacement of the plate and the beam, denoted by w0 and w1, then satisfies the following plate and beam equations (3-7) where m0 and F are the mass density per unit area and external force amplitude, respectively. The force from the joists is denoted by P1. The flexural rigidity, D0, for the plate is computed by E0h03/12( 1-ν2), where E0 is Young's modulus for the plate.
(3-8) where E1, I1 and m1 are Young's modulus for the beams, moment of inertia and the mass density (per unit length) of the beams, respectively. The moment of inertia is computed by h1 d1/12, where d1 is the thickness and the width of the beams. The forces acting on the plate and the beams (on the right hand side of the equation) will be explained in the following subsection. The differential operator is defined as
Note that the displacement of the beams are denoted by w1(x,j), j=1,2,,...,S1 for j'th beam. The above equations can be used for the dynamics of the LTF floor structure in the low frequency range (below 200Hz). In the higher frequency range, the characteristics of the wood change and such a linear model cannot represent the vibrations of the components adequately. Furthermore, the mechanical ambiguity in the structure plays great role in the higher frequency range. Thus the completely deterministic model cannot predict the dynamics of the structure. Coupling between the floor and the joists We here consider the coupling between the floor surface and the joist beams. We assume that the two components are linked by springs in the lateral direction along the joist beams. We also assume that the plate and the beams are always in contact. Hence, (3-9) where yj are the locations of the joists. We consider the elastic resistance between the floor and the joists as they bend then slip as depicted in figure 3-7. The figure describes the discrepancy in the lateral displacement of the floor, which will result in the resisting force at the joining layer. The resistance is assumed to be linear to the length of the slippage, which is determined by the slope of the beam (plate).
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Plate
}
h0 2
h0/w0 h1 dw1 2 /x 2 dx
}
h1 2
Beam
Figure 3-7: Schematic drawing of the cross-section of joining layer (floor-joists). The lateral displacement is given by the sum of the first derivatives of the displacement functions.
The resisting force between the plate and the beam is
(3-10) where σ is the spring constant along the joists. The gradient of the floor and the attached joists coincide because of equation (3-9). Hence we have the force acting on the plate and the beam
(3-11) where H= ( h0+ h1)/2. q1(x,j) denotes the vertical pressure at the contact surface between the upper plate and the j'th joist beam. The neutral plane of Kirchhoff plates and Euler beams do not stretch. Hence, the structure would not bend when there is no slippage, i.e., σ = ∞. We here assume that there is always some slippage. The vale σ is will e determined by comparing the theoretical results and the experimental data, which will be shown in later subsection. Fourier expansion method The system of equations (3-7)(3-8) with the conditions given by (3-9) and (3-10) can be solved using the Fourier sine-series expansion technique, since the floor and joists are assumed to be simply supported. We show how the coefficients of the expansion can be computed. Note that we use finite number of terms for the expansion because the expansion is intended for numerical computation. The displacement of the plate and the beams can be expanded as
(3-12)
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where Cmn0 Cjm1 are the unknown coefficient to be determined. The basis functions for the expansion are
The spatial wavenumbers are defined as km =π m/A and κn = π n/B. These functions satisfy the following orthogonal relationships
(3-13) We now substitute equations (3-12) into (3-7), (3-8) and (3-9), and use the orthogonal relationship given by equation (3-13). The system of equations for the coefficient of the sineexpansion is
(3-14) where
Equations (3-14) can now be solved numerically. Description of experiments The dimension of the experimental joist-floor structure is shown in figure 3-6. An electrodynamic shaker was used to provide a vertical force on the floor upper surface. The shaker was connected to the floor through a wire stinger and a reference force transducer. The shaker body was mounted on a beam that straddled the floor and rested on supports sitting on the concrete collar surrounding the floor. Vibration isolation was provided by very resilient pads. A scanning laser vibrometer (Polytec PSV 300) was used to measure the velocity of the floor normal to the surface. A grid with a spatial resolution of 10-14cm was used to obtain a map of the surface velocity of the floor relative to the input force; both amplitude and phase information was recorded at each frequency. The shaker was driven with pseudorandom signal with a bandwidth from 10 to 500Hz, and a length of 2 seconds (to get a frequency resolution of 0.5Hz). An accelerometer was also placed at the force transducer input to determine the input impedance of the floor. Computation results We here compare the theoretical results against the experimental measurements described above. The physical values used in the computation are, m0 = 0.015x500, m1 = 0.045x0.3x500, ν = 0.4 and damping ratio for the Young's modulus is 0.04. Two ways of modelling the damping effects are tried here, constant damping coefficient and frequency dependent damping coefficient for the Young's module.
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Mean square velocity (dB Ref 1e−8)
110 100 90 80 70 60 50
0
20
40
60
80
100 120 Frequency Hz
140
160
180
70
80
90
200
√, dB (re: 5x10 m/s)
40
−8
80 75 70
2
65 60 55 10
20
30
40
50 60 Frequency (Hz)
Figure 3-8: Normalized average velocity of the floor surface. (top)Theoretical results for various σ = 0 (dash), 5 * 106 (solid), 107 (dot) and 108 (dash-dot). (bottom) Experimental results.
Figure 3-8 (top) show that the slippage coupling in the model makes substantial difference to the location of the resonance frequencies. As noted in the previous section, the theoretical model breaks down when the resistance, σ, is large. In a timber structure, the effects of the damping are important. Although, there are many ways to model the damping, however complexity of the damping is outside the scope of this paper. We thus consider the damping as complex valued Young's module. The results in the figures in this section use E0=1010 ( 1+0.03i)Pa and E1=1.4x109Pa for the joist beams. One may choose frequency dependent damping, that is, the damping ratio is a function of the frequency. Figure 3-9 shows the measurements of the displacement of the floor surface at frequencies 22Hz, 23.5Hz and 27Hz. The theoretical model on the other hand gives 22.5Hz, 23.5Hz and 28Hz with σ = 5x106. The model however overestimates the displacement at the first two resonance frequencies and underestimates at the third resonance frequency. The reason for these discrepancies is yet to be identified.
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Figure 3-9: Measurements and the theoretical computation of the displacement at the first resonance frequencies. Note that different coordinate orientation is used for the experimental data and the theoretical computation.
Method of solution for multi-layered structures The Fourier expansion technique shown in the previous sections can be used to find the solutions of structures that are made of more components as depicted in figure 3-10 . We first introduce the notations for the parameters of each component. The layers are denoted by l=0,1,...,M, where the 0'th and the M'th are the upper plate and the ceiling. The layers l=1,2,...,M-1 are the beams that are places perpendicular from one layer to the next. Hence the beams run either in the x or the $y$ direction. The beams are connected by a vertical spring where they meet between the layers, and the spring constant at between the layers l and l+1 is denoted by τl, l=1,2,...,M-1.
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Figure 3-10: Schematic drawing of the cross-section of the floor structure. The origin of the coordinates is placed at the corner of the floor. The $z$-axis is pointing downwards.
We assume that the same contact conditions exist between the upper plate and the joist beams and the ceiling and the beams. The vertical 1-dimensional springs are used to between the beams in the layers l-1 and l, l=2,3,...,M. The number of beams can be different from a layer to a layer. There is a bottom plate (ceiling), which creates an enclosed cavity. The effects of the air must now be considered. Equations and Notations The displacement of the bottom plate, denoted by wM+1, and the beams wl ( x,j), satisfy the following plate and beam equations
(3-15) where the notations for the physical parameters follow the same rule given in the previous section. The air pressure on the bottom plate is denoted by p( x,y,d). The air pressure on the top plate is then p( x,y,0). The pressure between (l-1)'th and l'th layers depends on the difference of the vertical displacement of the beams. Denoting the spring constant by τl gives (3-16) Hence the right hand side of equation (3-15) is the sum of the above pressures where the beams in (l-1)'th, l'th and (l+1)'th layers. The acoustic pressure function, p( x,y,z), satisfies the Helmholtz equation (3-17) where c is the speed of sound for the air in the cavity space. This equation is then solved with the boundary conditions (see Cremer73) (3-18) and the normal derivative of p is zero on the cavity walls, that is, the walls are rigid. The divisions in the cavity by the beams are not considered here. Filling materials in the cavity can be modelled by modifying the parameters c and ω (see Bies and Hansen, 2003). Page 56
We here summarize the notations for the solution as there are numerous components in the structure.
Solution for the cavity air The solution of Helmholtz equation (3-17) can also expressed by the following expansion
Where so that the expansion satisfies the boundary condition at the cavity walls. The unknown function ξ (z) then satisfies the following ordinary differential equation,
Solving the above ordinary differential equation gives,
(3-19) where γmn=√(k m+κ n−k ). The coefficients Γmn and Γmn are to be found from (3-18) and the coupling conditions with other components in the structure. 2
2
2
(1)
(2)
The boundary conditions (3-18) give the following relationship between the coefficient.
(3-20) where
when m+m’ (n+n’) is odd, otherwise fA and fB are zero. Σ’ denote the summation over m,n,m',n'. The effects of the cavity-filling are taken into account using the formulae given in Bies and Hansen. Derivation of the system of equations for the coefficients Using (3-21) and (3-22) give
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(3-23) where H' = ( hM+hM+1) /2. The beam equation, using the notations given by (3-16), becomes
Equations for the whole structure We first define the vectors of unknown coefficients in order to formulate the matrix equations for them. The (column) vector notations C, P1 and P2 are defined as
The equations for the beams wl, l=1,2,...M-1, can be expressed by the following system of matrix equations.
(3-24) The rows of the above matrix represent the equations that are formulated in the previous subsections. The column vector cl is defined from the coefficients of the Fourier expansion of the beam deflection. The additional equation for the 1'st and the ( M-1)'th beams is
(3-25)
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Matrix elements MatLab codes have been written to directly implement the method of solution given in the previous sections. The codes are written to mimic the real structure as closely as possible, though there are compromises made because of the limitation in the theory. The mock-up floors considered here are built in real size and the surface velocity of the upper plate and the ceiling are measured as described in section 3. In order to reduce the size of the matrix, the system of equations in section 4 are solved for the coefficients of the upper plate and the ceiling, c0mn, cMmn. Hence the size of the matrix is 2N2x2N2. We here give a few examples of the elements of the matrices in equation (3-24).
for j=1,2,...,S1.
where [..]( (i,n),(j,m)), indicates the (i,n)'th row and the (j,m)'th column. The equations for the coefficients of the upper plate and the ceiling are written into the computer codes in the following form.
where and are the matrices derived from equations given in this subsection. R0 and RM are the diagonal matrices of Rm0 and RmM, respectively. 3.4
MODELLING FIBROUS INFILL.
Work has been done by a number of people to predict the effects fibrous materials have on sound propagation, where empirical and physical models have been produced. Bies and Hansen (2003) have produced a summary of aspects of this is their text book. Work by Delaney and Bazley in the late 1960’s resulted in an empirical model which was limited in accuracy both by frequency range and by flow resistivity. Bies and Hansen showed an empirical model which tends to the correct limits for both high and low values of ρ f / R1 , ρ being the air density, f the frequency and R1 the flow resistivity. Allard and Champoux have also published an empirical model for sound propagation through fibrous infill, the results of this model are similar to the Bies and Hansen model. These models, however, assumes that the fibrous material is in a rigid frame and hence is not moving with the motion of the air. Unfortunately, if the infill is not backed by some rigid frame it will move with the motion of the air.
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Bies and Hansen consider the case of transmission loss through fibrous material. They suggest that if the wavelength of the sound in the fibrous material is longer than ten times the depth of the fibrous material the fibrous material will start to move with the sound waves, resulting in reduced transmission loss through the infill. They provide a graph with which one can estimate the low-frequency transmission loss, based on the flow resistivity. To our knowledge, there is no effective information about how sound propagates through fibrous infill inside a cavity, given suitable information about the infill (e.g. flow resistivity, density), particularly at low frequencies. Effective models for sound transmission through walls often use some form of empirical model for the effect of the infill in the cavity, given information about the infill7. Of course, once such sound transmission models are given information about the acoustic properties of the infill they can work, but the question is how to get these properties from basic knowledge of the infill which is in the cavity. For the purpose of this project, we will use Bies and Hansen’s model to determine the sound propagation through the fibrous infill. Bies and Hansen’s model can give us the dimensionless bulk modulus κ and the dimensionless density ρm, which are used to calculate the complex speed of sound in the fibrous infill and its complex characteristic impedance. These parameters are functions of the sound frequency and the flow resistivity of the fibrous infill. We will use the experimental results to produce a low-frequency empirical estimate of the infill performance by making the flow-resistivity a function of frequency, producing a kind of rigidframe equivalent flow resistivity – the flow resistivity the fibrous infill would have had if it had not been moving with the sound waves . We expect that this equivalent flow resistivity will be quite low at very low frequencies and will rise to the normal flow resistivity when the wavelength of sound is less than one tenth of the thickness of the infill. One way of producing an empirical formulation for what might be called the ‘effective’ flow resistivity is by a linear interpolation between 0Hz where the transmission loss is apparently zero, and a ‘knee’ frequency where the transmission loss through fibrous infill starts to level off to a maximum – presumably indicating when the infill is no longer moving significantly with the sound wave. In their textbook, Bies and Hansen have published data showing the transmission loss through fibrous infill at low frequencies. For average flow resistances (400 to 8000 Rayls), we find that this knee frequency occurs when f ρB =K, R1 where f is the frequency, ρB is the density of the fibrous infill, R1 is the flow resistivity, and K is the knee point constant, which is about 2. Above this knee point the effective flow resistivity is R1 , and below this knee point the effective flow resistivity is given by Kρ B f . Note that for this empirical scheme, the important parameter for determining low-frequency effective flow resistivity is the density of the material rather than the flow-resistivity – of course, these two parameters are closely related for a given fibre size.
7
Ballagh, K., Private correspondence. Page 60
3.5
FURTHER COMPARISON OF THE FLOOR MODEL WITH EXPERIMENTAL RESULTS.
In this section we look at how the floor model compares with experimental results. We will also use the experimental data to set some parameters, particularly the slipping resistance of the joist to floor upper connection. Simple floor without ceiling. We first consider the case of a simple floor consisting of 15mm plywood screwed to 300mm deep LVL joists (which are at 400mm centres). The experimental test version of this floor is denoted ‘Floor 10’. We use the fundamental frequency and the frequency of the second bending mode along the joist direction to determine the slip resistance; this was found to be about 1.5×107 N/m2. The slipping resistance is not very sensitive to small changes and a 50% change makes little difference. Presumably the slipping resistance is related to the shear stiffness of the plywood and LVL joists as well as slipping between the two layers. The LVL joist Young’s modulus was taken to be 14.5GPa. It must be noted that wood stiffness (like all polymers) changes with frequency; higher frequencies give slightly higher stiffnesses. The second resonance frequency from the experimental results gives the dynamic bending stiffness of the plywood along the face grain direction; this was found to be equivalent to a 15mm deep homogeneous plate with a Young’s modulus of 12GPa. This can be compared to longitudinal resonance tests of the plywood which showed the along-grain dynamic Young’s modulus to be 13GPa. The loss factor of the LVL and the plywood was taken as 0.03. Figure 3-11 shows the average surface velocity of the experimental and theoretical models using the material properties set out above. They compare well. Differences in the frequency range below 100Hz are due to the panel nature of the plywood causing more complicated modes, giving smaller resonant peaks, whereas the model assumes a continuous layer of plywood. The differences in the frequencies above 100Hz are due to the locally reacting nature of the floor at the forcing point, resulting in large, non-propagating deflections over a small region. These large deflections are difficult to measure properly and so the experimental results may be somewhat inaccurate. Another thing that appears to be happening at frequencies above 100Hz is that the plywood is separating from the joists in the regions between the screws whereas the model assumes a continuous connection.
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2 √ , 5.5 x 3.2 m Floor 10 Upper, Fin=1 N at pos E.
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Figure 3-11. Experimental (a) and theoretical (b) results for the average upper surface velocity of floor 10. The floor is forced vertically at one point on the floor (denoted position ‘E’ – 0.965m from one side and 1.875m from one end of the floor) and results normalised so that the force has an amplitude of 1N for all frequencies.
Simple floor with plasterboard ceiling on resilient clips. This floor is an extension of the previous floor (as well as being of a different span). It has a ceiling consisting of two layers of 13mm plasterboard screwed to pressed-steel ceiling Page 62
battens at 600mm centres, which are attached to every other joist (i.e. at 800mm centres) through resilient clips (RSIC-1 rubber clips). The model assumes that there is a ceiling clip on every joist – this is compensated for by reducing the stiffness of each clip by a suitable amount. The cavity is 358mm deep and is infilled with 2 layers of 150mm sound control type fibreglass batts (Tasman Insulation Midfloor Silencer). The experimental, test version of this floor is denoted ‘Floor 10’. The ceiling battens are Gib Rondo battens 35mm deep and have a calculated stiffness of 11000 Nm2. The ceiling batten resilient clips have a measured stiffness of 220000 N/m with a 130N constant load, and a loss factor of about 0.1. The infill has a flow resistivity of 7227 Rayls/m and a density of 12 kg/m3. The plasterboard layers are assumed (through experimental observation) to be slipping and have an isotropic Young’s modulus of 3.7 GPa, a density of 962 kg/m3, and a loss factor of 0.013. For simplicity, the model assumes that the ceiling material stiffness is isotropic, although this is generally not the case. Figure 3-12 shows the average surface velocity of the ceiling of the experimental and theoretical models using the material properties set out above. They compare well, except for frequencies above 100Hz, where it is suspected that the plywood may be separating from the joists, making the model less valid for this case.
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2 √ , 7 x 3.2 m Floor 2 ceiling, Fin=1 N at pos C.
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Figure 3-12. Experimental (a) and theoretical (b) results for the average ceiling velocity of floor 2. The floor is forced vertically at one point on the floor (denoted position ‘C’ – 0.965m from one side and 2.510m from one end of the floor) and results normalised so that the force has an amplitude of 1N for all frequencies.
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Floor with three gypsum fibreboard layers screwed to plywood. This floor is the same as the previous floor (Floor 2), but has three layers of 12.7mm Gib Sound Barrier (a proprietary gypsum fibreboard) screwed to the upper surface of the floor (i.e. the plywood). We compare this floor with the model results to see the effect of having extra stiff layers on the upper surface of the floor. The gypsum fibreboard is assumed to have a Young’s modulus of 4.5GPa, a density of 1040 kg/m3 and a loss factor of 0.04. The gypsum fibreboard has a reported increased loss factor due to interactions between the layers; in comparison, the material loss factor of the gypsum fibreboard itself is about 0.01. It assumed that the gypsum fibreboard layers are nonslipping and bend together (with the plywood) as one unit. Figure 3-13 shows the average surface velocity of the ceiling of the experimental and theoretical models using the material properties set out above. They compare well, except for some of the resonances above 100Hz. Exploration with the model shows that these resonances are caused by the ceiling battens; their height is related to the ceiling batten stiffness, and their spacing in frequency due to the ceiling plasterboard properties.
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2 √ , 7 x 3.2 m Floor 3 ceiling, Fin=1 N at pos C.
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(b) Figure 3-13. Experimental (a) and theoretical (b) results for the average ceiling velocity of floor 3. The floor is forced vertically at one point on the floor (denoted position ‘E’ – 0.965m from one side and 1.875m from one end of the floor) and results normalised so that the force has an amplitude of 1N for all frequencies.
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Floor with 85mm of sand/sawdust between plywood on upper surface. This floor is the same as Floor 2, but has 90mm deep battens screwed to the upper plywood of the floor (at right angles to the joists) with another layer of plywood on the battens. Between the battens is an 85mm layer of paving sand with sawdust at an 80/20 mix by volume. We compare this floor with the model results to see the effect of having a large amount of mass, stiffness and damping on the upper surface of the floor. The model is not able to model the upper surface exactly as built, but is able to model an equivalent single upper surface plate with rib stiffeners running perpendicular to the joists. Experimental results (namely the position of the second resonance peak) tell us about the stiffness of this plate. Looking at the decay of the vibrations along the upper surface of the floor we can estimate the loss factor of the upper surface plate (consisting of sand/sawdust and plywood with battens); at 100Hz and above we estimate the loss factor to be between 0.4 and 0.8, at the fundamental resonance we estimated the loss factor to be less than 0.1. Noting from the work of others that the loss factor of sand layers changes with frequency, we assume that the loss factor of the upper floor surface linearly changes from 0 at 0Hz to 0.8 at 200Hz. This is a simplification of a not very well understood phenomenon. Figure 3-14 shows the average surface velocity of the ceiling of the experimental and theoretical models using the material properties set out above. They compare well, except for some of the resonances between 30 and 50Hz. This is probably due to inaccuracies of the estimated loss factor due to the sand and sawdust fill.
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2 √ , 5.5 x 3.2 m Floor 9 ceiling, Fin=1 N at pos E.
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(b) Figure 3-14. Experimental (a) and theoretical (b) results for the average ceiling velocity of floor 9. The floor is forced vertically at one point on the floor (denoted position ‘E’ – 0.965m from one side and 1.875m from one end of the floor) and results normalised so that the force has an amplitude of 1N for all frequencies.
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Floor with 400mm I-beam joists. This floor has 400mm deep I-beam joists at 600mm centres, with a 20mm particleboard upper surface. It has a ceiling consisting of two layers of 13mm plasterboard screwed to pressed-steel ceiling battens at 600mm centres, which are attached to every other joist (i.e. at 1200mm centres) through resilient clips (RSIC-1). The cavity is 458mm deep and is infilled with 3 layers of 150mm sound control type fibreglass batts (Tasman Insulation Midfloor Silencer). The experimental version of this floor is denoted ‘Floor 18’. We compare this floor with the model results to see the effect of having a deeper floor with deep I-beams: deep Ibeams have a significant amount of web shear as a component of their deflection performance (around 40% for the 400mm deep I-beams used), whereas the model assumes infinite shear stiffness. It is assumed that the I-beams have a bending stiffness of 3494000 Nm2, and the particleboard has a Young’s modulus of 4 GPa with a density of 710 kg/m3. Figure 3-15 shows the average surface velocity of the ceiling of the experimental and theoretical models using the material properties set out above. They compare well, considering that the model only considers the joists to have a bending stiffness contribution. Resonances are also clearer in the model at the frequencies above 100Hz, suggesting that there is more vibration damping in the real structure than that modelled.
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2 √ , 5.5 x 3.2 m Floor 18 ceiling, Fin=1 N at pos E.
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(b) Figure 3-15. Experimental (a) and theoretical (b) results for the average ceiling velocity of floor 18. The floor is forced vertically at one point on the floor (denoted position ‘E’ – 0.965m from one side and 1.875m from one end of the floor) and results normalised so that the force has an amplitude of 1N for all frequencies.
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General Comments. Overall the model seems to compare well to experiment: it predicts the fundamental and second mode resonances well and follows the general trends correctly, suggesting that using the model to predict overall averages would be quite accurate. The model can’t be an exact comparison because it is a simplified version of the real thing, and because we don’t know enough about the parameters of the materials we used for experimental comparison, especially since some properties change with frequency. It could be possible to make a more complicated model which more closely resembles reality. However, such a model would involve having to specify even more material properties, which would be very time consuming to determine. 3.6
PART III: MODELLING THE RECEIVING ROOM.
One of the important aspects of low-frequency sound transmission is the effect of the receiving room on the sound generated by the vibrating floor/ceiling system. There is a reasonable amount of literature on the subject of how room size and dimension affects performance of airborne sound transmission through walls, but not a lot about impact sound transmission through floors. For our purposes, we would like to predict the sound pressure generated by the vibrating ceiling in the room below; one aim would be to find the average sound pressure in this so-called receiving room. We note that many researchers assume an infinitely-sized room and essentially look at the sound power radiated by the ceiling. This infinitely large room approach does not consider the effects the resonances in the room have on the sound pressure generated by the vibrating ceiling; this approach also does not consider the effects near-field radiation might have. For example, even vibrating modes do not generate much radiated sound power in an infinitely-sized room, but nearer to the ceiling there is a lot sloshing of air backwards and forwards between peaks and troughs in the ceiling vibration, and this must contribute to the sound pressure detected in the receiving room. Although not much exists on this subject, it is not difficult to predict the sound pressure generated in a room by a vibrating ceiling if one makes suitable approximations. We basically assume that the room is a rectangular box with a uniform absorption of sound energy over its surface. The theory. The theory of the room is based on work published by Morse and Ingard (1986,section 9.4). For a ceiling with surface displacement w( x ′, y ′) vibrating at frequency ω, the sound pressure in the room below is given by p rec ( x, y, z ) = − ρω 2 ∫∫ G ( x, y, z | x ′, y ′) w( x ′, y ′)dS ′ , lxl y
where x, y and z is a point in the room, lx and ly are the dimensions of the floor, ρ is the air density, and S’ is the ceiling surface with x’ and y’ being location of a point on the ceiling. G is the Green’s function which describes the propagation in the room as is given by πn x πn y y πn z z πn x′ x ′ πn y ′ y ′ cos cos cos cos x cos l l l′ l′ ∞ l x y z x y , G ( x, y , z ) = ∑ V Γn (k n2 − k 2 − iτ n ) nx n y nz where nx, ny and nz are the mode numbers of the room in the x, y and z directions respectively (n being a short form of this i.e. n = {n x , n y , n z } ), V is the room volume, k is the wavenumber. Also
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k n2 = k nx2 + k ny2 + k nz2
β x 0 + β xl lx
τ n = k ε nx
; k nx =
πn x lx
, k ny =
β + β yl + ε nx y 0 ly 1 Γn =
πn y ly
, k nz =
πn z lz
+ ε nx β z 0 + β zl lz
,
,
ε nx ε ny ε nz
where the β’s are the surface admittances on each of the six surfaces of the room, and 1 , n y = 0 1 , n x = 0 1 , n z = 0 ε nx = , ε ny = , ε nz = . 2 , > 0 n n 2 , > 0 y z 2 , n x > 0 To simplify things, we assume that the surface admittance is the same on all surfaces. For random incidence of sound we can also assume that the surface admittance and the absorption coefficient of the room surfaces are related by (Morse and Ingard, 1986, p 580) α = 8 Re{β } . We can use the above formulation to calculate the sound pressure inside the room, and by selecting a large number of points (typically several hundred) and averaging them, we can find the average sound pressure inside the receiving room.
Testing the receiving room model. There are a number of ways to confirm the accuracy of the theory and resulting code: you can examine the low-frequency limits in the room, and you can model a monopole at the corner of the floor for a number of limiting situations. These were done to confirm that the model works. One can also compare prediction to measurement for the sound pressure generated by a floor on a room. This was done for a rectangular room measuring 3.2m by 3.6m by 3.05m high. It had plasterboard walls and a concrete floor. The floor also measured 3.2m by 3.6m, and was particleboard type floor. The vibration of the underside of the floor was measured by accelerometers in a grid patterns with a resolution of 200mm. The resulting accelerations where normalised against the force produced by an excitation hammer (including phase information). Inside the room the sound pressure was measured by microphone at 25 measurement points across the volume of the room. Figure 3-16 shows the resulting comparison of measured average sound pressure in the room and the sound pressure predicted by the model using the measured vibrations of the underside of the floor above the room. The absorption coefficient of the room was assumed to be 0.15 for the model, based on work by Maluski and Gibbs (2004), and 200 random points were averaged inside the model room. There is a good correspondence between the model and the measurement, considering that relatively few sound pressure measurement points were used inside the room. We also must realise that the model is a sort of ideal room and no real room matches it exactly, but at low frequencies there is a good correspondence at we are able to use it to indicate what is likely to happen in a real room.
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, 3.6 x 3.2 m floor, 3.05m room height, Fin=1 N. 90
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3.7
REFERENCES
Allard, J-F, Champoux, Y., (1992). New empirical equations for sound propagation in rigid frame fibrous materials, J. Acoust. Soc. Am. 91 (6). Ashton, J.E. and Whitney, J.M. (1970), Theory of Laminated Plates, Technomic Publishing Co, Stamford, Conn. Australian Standard, Standard Australia, 1993. Bies, D.A. and Hansen, C.H. (1988) Engineering Noise Control, Theory and practice, Unwin Hyman Ltd., London Bies, D. A. and Hansen, C. H., (2003). Engineering Noise Control: Theory and Practice, 3rd Edition. Blazier, W.E. and DuPree, R.B. (1994) “Investigation of low-frequency footfall noise in woodframe, multifamily building construction”, J. Acoust. Soc. Am., 96, pp. 1521--1532. Brunskog, J. (2002) Acoustic Excitation and Transmission of Lightweight Structures, PhD thesis, Lund University. Craik, R.J.M. and Smith, R.S. (2000) “Sound transmission through double leaf lightweight partitions part {I}: Airborne sound”, Applied Acoustics, 61, pp. 223--245. Page 73
Craik, R.J.M. and Smith, R.S. (2000) “Sound transmission through lightweight parallel plate. part {II}: Structure-brone sound”, Applied Acoustics, 61, pp. 247--269. Craik, R.J.M. and Wilson, R. (1996), “Sound transmission through parallel plates coupled along a line”, Applied Acoustics, 49, pp. 353--372. Cremer, L. Heckl, M. and Ungar, E. (1973) Structure-Borne Sound, Springer-Verlag, New York. Emms, G (2004) “The effect of mounting conditions on low-frequency impact sound insulation of timber floors”, ICA porceedings, April. Emms, G. and Hollows, R. (2002) “Using sound intensity to measure the impact insulation of floors”, in The 2002 International Congress and Exposition on Noise Control Engineering, August. Evseev, V.N. (1973) “Sound radiation from an infinite plate with periodic inhomogeneities”, Soviet Physics Acoustics, 19, pp. 345--351. Fahy,F.S. (1985) Sound and Structural Vibration, Academic Press Ltd., London. Hammer, P. (1996) “Vibration isolation on light weight floor structures”, Tech. Report TVBA3078, Department of Engineering Acoustics, Lund University. Langley, R.S. and Heron, K.H. (1990) “Elastic wave transmission through plate/beam junctions”, Journal of Sound and Vibrations, 143, pp. 241--253. Langley, R.S. Smith, J.R.D. and Fahy, F.J. (1997) “Statistical energy analysis of periodically stiffened damped plate structures”, J. Sound and Vibration, 208, pp. 407--426. Lin, G. and Garrelick, J.M. (1977) “Sound transmission through periodically framed parallel plates”, J. Acoust. Soc. Am., 61, pp. 1014--1018. Mace, B.R. (1980) “Sound radiation from a plate reinforced by two sets of parallel stiffeners”, Journal of Sound and Vibration, 71, pp. 435--441. Mace, B.R. (1980) “Periodically stiffened fluid-loaded plates, {I}: Response to convected harmonic pressure and free wave propagation”, Journal of Sound and Vibration, 73, pp. 473-486. Mace, B.R. (1980) “Periodically stiffened fluid-loaded plate, {II}: Response to line and point forces”, Journal of Sound and Vibration, 73, pp. 487--504. Maluski, S., Gibbs, B.M. (2004). “The effect of construction material, contents and room geometry on the sound field in dwellings at low frequencies,” Applied Acoustics, 65, pp 31-44. Mead, D.J. and Pujara, K.K. (1971) “Space-harmonic analysis of periodically supported beams: Response to convected random loading”, Journal of sound and vibration, 14, pp. 525-541.
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Morse, P. and Ingard, K. (1968) Theoretical Acoustics, McGraw-Hill, New York. Morse, P.M., Ingard, K.U. (1986), Theoretical Acoustics, Princeton University Press. Section 9.4. Rumerman, M (1975) “Vibration and wave propagation in ribbed plates”, J. Acoust. Soc. Am., 57, pp. 370--373. Takahashi, D. (1983) “Sound radiation from periodically connected double-plate structures”, Journal of Sound and Vibration, 90, pp.541--557. Yairi, M., Sakagami, K., Sakagami, E., Morimoto, M., Minemura, A. and Andow, K. (2002) “Sound radiation from a double-leaf elastic plate with a point force excitation: Effect of an interior panel on the structure-borne sound radiation”, Applied Acoustics, 63, pp. 737--757. Zaher, A. (2004) “Development of a wooden joist floor with high impact sound insulation”, Tech. Report, Acoustics Research Centre, The University of Auckland.
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4 FLOOR MODEL ANALYSIS 4.1
INTRODUCTION.
In this chapter we consider results obtained from the theoretical floor (and room) model. One of the problems we face in doing this is that there are many variables which can be altered to produce a multidimensional space within which we search for some solution. The solution we are looking for being the matching of the low-frequency performance of a joist floor to that of a 150mm thick concrete floor. Since the possibilities are almost endless and the variables aren’t independent, we will attempt to examine the effect of changing various variables by starting with a model of a timber floor which, by today’s standards (in Australasia, that is), performs reasonably well in the area of low-frequency impact insulation. This floor is the floor designated ‘Floor 3’, with the exception being that it has a span of 5.5m. It consists of 38mm of Gypsum Fibreboard screwed onto a plywood subfloor with 300mm deep LVL joists and a plasterboard ceiling consisting of 2 layers of 13mm dense plasterboard connected to the ceiling via rubber resilient clips; the ceiling cavity is filled with sound control fibreglass. This floor spans 5.5m and is 3.2m wide, and is on a rectangular room 2.4m deep with an average surface sound absorption coefficient of 0.15. With the model of ‘Floor 3’ with all its parameters as the starting point, we then vary certain parameters of the floor while holding the rest constant. This enables us to observe the effects of changing these parameters in a theoretical way to produce indications of trends. There are many parameters to consider, so in order to package the results up into more digestible packages, we divide the floor up into four different sections:• The joists. • The upper surface or floor upper, consisting of everything that exists on top of the joists. • The cavity, consisting of everything that acoustically connects the floor upper to the ceiling (this includes ceiling clips and battens). • The ceiling. We also consider one further aspect of the floor: the span of the floor and other dimensions associated with the floor and the room beneath. In each section, we consider a number of apparently important parameters by varying each parameter in turn. For each parameter we produce low-frequency spectra of the predicted average vibration levels on the ceiling and the predicted average sound pressure levels in the receiving room. These spectra are for a force of 1N averaged over 10 forcing positions distributed over the floor. 4.2
SINGLE FIGURE RATINGS.
Producing vibration and sound pressure spectra as the floor properties are varied is useful to see what aspects of the spectra are changing, but it is also useful to obtain single figure ratings for each floor. To do this, we go to the knowledge gained in the subjective analysis we’ve done in this project which gave us a subjective correlation between loudness of impact sounds and subjective desirability for the floor. We will, therefore, consider the Loudness produced by two different low-frequency dominated impacts:1) Idealised footstep 2) Japanese standard ball drop. To produce these numbers, we get the spectra of sound pressures in the receiving room we calculate for each floor, and multiply them by the force spectra of the two impacts. We are
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limited to frequencies below 200Hz for the modelling; hence the loudness ratings are restricted to frequencies below 200Hz with higher frequencies assumed to have no contribution. These low-frequency single figure ratings enable us to produce simple plots of floor performance against the parameter we are changing. One purpose of these low-frequency single figure ratings is to enable comparison with the performance of a 150mm deep concrete floor. To achieve this, such a concrete floor was modelled and the corresponding frequency spectra and single figure ratings produced. These ratings are also shown on the plots. As with all single figure ratings, care has to be exercised: much information can be lost when generating a single figure rating. So while one can obtain a general feel for trends, it is always wise to look at the full spectrum plots to observe in more detail what is happening. The force produced by the Japanese Impact Ball. The force produced by the Japanese Ball (Rion Impact Ball YI-01) was measured using an impact plate mounted on a force transducer which was mounted on another plate sitting on a concrete floor. The manufacturers of the ball provide a calibration sheet with a recording of the impact signal produced by the ball without absolute determination of the forces produced. This experimental set-up was used to calibrate the amplitude and duration of the pulse. From experimental recordings the impact pulse duration was 20msec (± 0.5msec), the peak amplitude 1400 N (± 50N), and peak location at 8.5msec from the start of the pulse. Figure 4-1 shows the resulting time domain pulse and spectrum.
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Force produced by a Japanese Ball dropped from 1m. 1500
Force (N)
1000
500
0
0
5
10
15
20
25 30 Time (ms)
35
40
45
50
(a) Frequency Response of a Japanese Ball dropped from 1m. Every 2 seconds 40
Ampliude of Force (dB re. 1N)
20
0
-20
-40
-60
-80
-100 1 10
(b)
2
3
10
10 Frequency (Hz)
Figure 4-1. Plots of the time response and frequency response of an impact produced by a Japanese Ball (Rion Impact Ball) dropped from 1m above the floor. The frequency response assumes the ball drop is repeated every 2 seconds.
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The force produced by footsteps. We assume from measurements made by Shi et al.(1997) that the forces produced by a footstep of a 80kg person in soft shoes are given by Figure 4-2. This is an averaging of the results presented by Shi et al. the first peak is assumed to be the heel strike and the second is the toe push off. The corresponding spectrum is shown in Figure 4-3. Force produced by a footstep (soft shoes) of 80kg person. 500 450 400 350
Force (N)
300 250 200 150 100 50 0
0
200
400
600
800
1000 1200 Time (ms)
Figure 4-2. The force produced by a footstep as a function of time.
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1400
1600
1800
2000
Frequency Response of a Footstep of a 80kg person on Bare Floor 40
Ampliude of Force (dB re. 1N)
20
0
-20
-40
-60
-80
-100 1 10
2
3
10
10 Frequency (Hz)
Figure 4-3. The force spectrum produced by a footstep.
In Shi et al. we find that tests were done on people of different weights, resulting in a correlation between the size of the peaks and the mass of the person. (viz. f max = 5.35(mass ) + 64.09 ). It is assumed that the speed of walking is 1.5 steps per second, so that by also assuming coherent addition of footstep forces (amplitude addition) we get a gain of 3.5dB on the previous spectra (Figure 4-3). It is worth noting that Blazier and duPree (1994) have some limited results about the influence of the speed of walking on results. Faster walking produces greater increases in sound level because of both the increase in step frequency and because of the greater peak forces produced by such impacts – the tendency is towards greater higher frequency levels because of the shorter duration of the impacts, as is also shown in results by Shi et al. (1997).
4.3
150MM CONCRETE REFERENCE FLOOR.
For reference purposes, it useful to have the low-frequency impact insulation results for a 150mm concrete slab. Modelling such a slab at low-frequencies is relatively easy, since it is essentially a homogeneous plate. We assume that the concrete is dense concrete with a density of 2300 kg/m3 and a Young’s modulus of 27 GPa. Although concrete in itself has very low internal damping (loss factors of around 0.006), the slab is assumed to be part of a building and hence can lose its energy to the rest of the building. Work by Koizumi et al. (2002) suggests that such a slab should have a loss factor of 0.06, when considering the energy lost to the rest of the structure. The slab is assumed to have the same size as the joist floors we are comparing it against (mostly 3.2 x 5.5m), and sits on the same room with the same height and acoustic properties (often 2.4m high with an absorption coefficient of 0.15). For example, the results of a concrete
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slab 3.2 x 5.5m on a room 2.4m high with an absorption coefficient of 0.15 are shown in Figure 4-2 and Figure 4-3. Using an absorption coefficient of 0.15 assumes that the room has plasterboard walls. A bare room with masonry walls will have an absorption coefficient which is much lower (around 0.02). It is thus to be realised that by taking the loss factor of the slab to be 0.06 and the absorption coefficient of the room under the floor to be 0.15 we are assuming a best possible situation for the concrete floor – the impact insulation performance will be worse for a concrete floor in isolation with masonry walls below. Average Ceiling Surface Vel - Concrete Floor (150mm) 55
Surface Vel rms (dB: re. 5e-8 m/s)
50
45
40
35
30
25
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-4. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Concrete Floor (150mm) 60
Sound Pressure (dB: re. 2e-5 Pa)
55
50
45
40
35
30
25
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-5. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
4.4
FLOOR JOIST PROPERTIES
In this section we consider the influences of the parameters of the floor joists on the floor performance.
Changing the bending stiffness of the joists. In this section we look at what happens when the joist bending stiffness is changed. For reference, a 300 by 45mm 14.5GPa joist has a bending stiffness of 1468100 Nm2.
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Average Ceiling Surface Vel - Varying Bending Stiffness of Joists 80 183513 Nm2 367025 Nm2 734050 Nm2
Surface Vel rms (dB: re. 5e-8 m/s)
70
1468100 Nm2 2936200 Nm2 60
5872400 Nm2 11744800 Nm2
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-6. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
Average Room Sound Pressure -Varying Bending Stiffness of Joists 90 183513 Nm2 367025 Nm2
80 Sound Pressure (dB: re. 2e-5 Pa)
734050 Nm2 70
1468100 Nm2 2936200 Nm2
60
5872400 Nm2 11744800 Nm2
50 40 30 20 10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-7. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
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Varying Bending Stiffness of Joists 14 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
12
Loudness (Sones)
10
8
6
4
2
0
0
2
4
6
8
10 2
Bending Stiffness of each Joist (Nm )
12 6
x 10
Figure 4-8. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
Changing the vibrational damping of the joists. In this section we examine the effect of changing the vibrational damping of the joists. Timber normally has a damping loss factor of 0.03.
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Average Ceiling Surface Vel - Varying Vibrational Damping of Joists 80 0.00 0.01 0.03 0.05 0.10 0.20 0.40
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-9. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
Average Room Sound Pressure -Varying Vibrational Damping of Joists 80 0.00 0.01 0.03 0.05 0.10 0.20 0.40
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-10. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
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Varying Vibrational Damping of Joists 12
Loudness (Sones)
10
8
6
Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
4
2
0
0
0.05
0.1
0.15 0.2 0.25 Loss factor of Joists
0.3
0.35
0.4
Figure 4-11. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
Inclusion of transverse stiffening across joists. One way to stiffen up a floor is to add transverse stiffening by way of blocking between joists, which has been clamped together with tie rods – such a series of blocking clamped with a tie rod is termed a ‘transverse stiffener’. In this section we look at the effect of an even spacing of transverse stiffeners along the floor; we vary the total number of transverse stiffeners along the 5.5m length of the floor. It was presumed that the effectiveness of transverse stiffening relies upon the transverse stiffening reducing the density of modes at higher frequencies, thus reducing the overall vibration levels. We expect that the effectiveness of reduction of modal density to be more challenging at greater floor widths. To test this idea of transverse stiffening we consider two cases:1) A floor 3.2m wide (Figure 4-12 to Figure 4-14) 2) An extremely wide floor 10m wide (Figure 4-15 to Figure 4-17).
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Average Ceiling Surface Vel - Varying Number of Transverse Stiffeners 70
Surface Vel rms (dB: re. 5e-8 m/s)
60
50
40
30
0 1 2 3 4 5
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-12. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
Average Room Sound Pressure -Varying Number of Transverse Stiffeners 70 0 1 2 3 4 5
Sound Pressure (dB: re. 2e-5 Pa)
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-13. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
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Varying Number of Transverse Stiffeners 14
12
Loudness (Sones)
10
8
6 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
4
2
0
0
0.5
1
1.5 2 2.5 3 3.5 Number of Transverse Stiffeners
4
4.5
5
Figure 4-14. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
Surface Vel rms (dB: re. 5e-8 m/s)
Average Ceiling Surface Vel - Varying Number of Transverse Stiffeners (floor 10m wide) 60 0 1 55 2 3 50 4 5 45 40 35 30 25 20 15
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-15. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Sound Pressure (dB: re. 2e-5 Pa)
Average Room Sound Pressure -Varying Number of Transverse Stiffeners (floor 10m wide) 70 0 65 1 2 60 3 4 55 5 50 45 40 35 30 25 20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-16. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Number of Transverse Stiffeners (floor 10m wide) 8 7
Loudness (Sones)
6 Footsteps (80kg person) Japanese Ball Drop
5 4 3 2 1 0
0
0.5
1
1.5 2 2.5 3 3.5 Number of transverse stiffeners
4
4.5
5
Figure 4-17. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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4.5
FLOOR UPPER LAYER PROPERTIES
In this section we consider the effects of the parameters of the floor upper – this is the part of the floor which lies on the joists, and stops people form falling through to the room below. Changing the surface density of upper surface of the floor. In this section the effect of changing the surface density of the floor upper is observed. Only the surface density is changed; we keep the bending stiffness of the floor upper equal to that of 3 layers of GFB on plywood found on Floor 3. For reference, the surface density of the floor upper of Floor 3 is 48 kg/m2, and 150mm of dense concrete is about 350 kg/m2. Average Ceiling Surface Vel - Varying Surface Density of Upper 80 10 kg/m2 20 kg/m2 40 kg/m2 80 kg/m2 120 kg/m2 160 kg/m2 200 kg/m2 240kg/m2
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-18. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Surface Density of Upper 80 10 kg/m2 20 kg/m2 40 kg/m2 80 kg/m2 120 kg/m2 160 kg/m2 200 kg/m2 240kg/m2
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-19. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Surface Density of Upper Surface Layer 15
Loudness (Sones)
Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete 10
5
0
0
50
100
150
200
250
2
Surface Density of Upper Surface (kg/m )
Figure 4-20. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Changing bending stiffness of the upper surface of floor. In this section the effect of changing the bending stiffness of the floor upper is observed. Only the bending stiffness is changed; we keep the surface density of the floor upper equal to that of 3 layers of GFB on plywood found on Floor 3. For reference, the bending stiffness of 20mm particleboard is about equal to 2000 Nm, and 150mm of dense concrete is about 11x106 Nm. Average Ceiling Surface Vel - Varying Stiffness of Upper 80 2000.000 Nm, 18000.000 Nm, 162000.000 Nm, 486000.000 Nm, 1458000.000 Nm
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-21. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Stiffness of Upper 80 2000.000 Nm, 18000.000 Nm, 162000.000 Nm, 486000.000 Nm, 1458000.000 Nm
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-22. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Bending Stiffness of Floor Upper 12
Loudness (Sones)
10
8
6 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
4
2
0
0
5 10 Bending Stiffness of Upper Surface (Nm)
15 5
x 10
Figure 4-23. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Changing the vibration damping of the upper surface of floor. In this section the effect of changing the vibrational damping of the floor upper is observed. For reference, we expect the damping loss factor of the upper of Floor 3 to be about 0.04.
Average Ceiling Surface Vel - Varying Damping of Upper 80 0.000 , 0.025 , 0.050 , 0.100 , 0.200 , 0.400 , 0.800
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-24. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Damping of Upper 80 0.000 , 0.025 , 0.050 , 0.100 , 0.200 , 0.400 , 0.800
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-25. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Damping of Floor Upper 12
Loudness (Sones)
10
8
6 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
4
2
0
0
0.1
0.2
0.3 0.4 0.5 Loss Factor of Floor Upper
0.6
0.7
0.8
Figure 4-26. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Changing the number of layers of gypsum fibreboard on the floor upper. In the previous sections where we looked at the floor upper we changed one parameter and somewhat artificially held other parameters constant. In this section we look at what happens when we increase the depth of the gypsum fibreboard on the plywood – we are changing both the surface density and bending stiffness of the floor upper. The gypsum fibreboard has a Young’s modulus of 4.5GPa and a density of 1040 kg/m2. Each board is 12.7mm thick, and it is assumed that they are screwed down so that the layers do not slip when bent. Average Ceiling Surface Vel - Varying Number of GFB Topping Layers 80 0 1 2 3 4 6 8
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-27. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Number of GFB Topping Layers 80 0 1 2 3 4 6 8
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-28. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Number of GFB Topping Layers 14
12
Loudness (Sones)
10
8
6 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
4
2
0
0
1
2
3
4 5 Number of layers
6
7
8
Figure 4-29. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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4.6
CAVITY AND CEILING CONNECTION PROPERTIES
In this section we consider the effects of the parameters of the region which acoustically joins the floor upper and the ceiling. This covers the cavity, its infill, and the properties of the ceiling clips and ceiling battens.
Changing cavity depth. In this section we look at the effect varying the cavity depth has on the floor’s performance. Normal cavity depths might range from 200mm to 400mm.
Average Ceiling Surface Vel - Varying Depth of Cavity 90 0.000 m 0.100 m 0.200 m 0.300 m 0.400 m 0.600 m 0.800 m
Surface Vel rms (dB: re. 5e-8 m/s)
80
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-30. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Depth of Cavity 90 0.000 m 0.100 m 0.200 m 0.300 m 0.400 m 0.600 m 0.800 m
Sound Pressure (dB: re. 2e-5 Pa)
80
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-31. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Depth of Cavity 18 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
16
Loudness (Sones)
14 12 10 8 6 4 2 0
0
0.1
0.2
0.3
0.4 0.5 0.6 Cavity Depth (m)
0.7
0.8
0.9
1
Figure 4-32. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Changing absorption of cavity infill. In this section we look at the effect of varying the acoustic absorption of the cavity infill. We assume that the cavity is completely full of infill, and we change the flow resistivity of the infill. For reference, normal fibreglass used for thermal insulation (e.g. Pink Batts) has a flow resistivity of about 1600 Rayls/m, whereas sound control fibreglass infill can have a flow resistivity of about 7000 Rayls/m. Average Ceiling Surface Vel - Varying Absorption of Cavity 80 0 Rayls/m 125 Rayls/m 250 Rayls/m 1000 Rayls/m 4000 Rayls/m 8000 Rayls/m
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-33. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Absorption of Cavity 80
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
0 Rayls/m 125 Rayls/m 250 Rayls/m 1000 Rayls/m 4000 Rayls/m 8000 Rayls/m
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-34. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Absorption of Cavity 14
12
Loudness (Sones)
10
8
6 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
4
2
0
0
1000
2000
3000 4000 5000 Flow Resistivity Rayls/m
6000
7000
8000
Figure 4-35. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Changing ceiling clip stiffness. In this section we examine the effect of changing the stiffness of the ceiling clips. It is assumed that there is a ceiling clip under every joist for every batten (rather than every other batten, as is normal – a constraint of the floor model), so for this floor we have ceiling clips at 400mm centres along the ceiling batten. For reference, a RSIC-1 clip has a stiffness of 220000 N/m, which for the model is reduced to about half that value since they are attached at 800mm centres (every other joist). Average Ceiling Surface Vel - Varying Stiffness of Ceiling clips 80 0.000 N/m, 50000.000 N/m, 100000.000 N/m, 200000.000 N/m, 400000.000 N/m, 800000.000 N/m, 100000000.000 N/m
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-36. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Stiffness of Ceiling clips 80
0.000 N/m, 50000.000 N/m, 100000.000 N/m, 200000.000 N/m, 400000.000 N/m, 800000.000 N/m, 100000000.000 N/m
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-37. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Stiffness of Ceiling Clips 18 16
Loudness (Sones)
14 12 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
10 8 6 4 2 0
0
1
2
3 4 5 Ceiling Clip Stiffness (N/m)
6
7
8 5
x 10
Figure 4-38. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Changing the vibrational damping of the ceiling clips. In this section we examine the effect of changing the vibrational damping of the ceiling clips. For reference, the RSIC-1 clips, which are rubber, have a damping coefficient of about 0.1.
Average Ceiling Surface Vel - Varying Vibrational Damping of Ceiling Clips 75 0.00 0.03 0.05 0.10 0.20 0.40 0.80
Surface Vel rms (dB: re. 5e-8 m/s)
70 65 60 55 50 45 40 35 30 25
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-39. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
Page 105
Sound Pressure (dB: re. 2e-5 Pa)
Average Room Sound Pressure -Varying Vibrational Damping of Ceiling Clips 80 0.00 0.03 0.05 70 0.10 0.20 0.40 60 0.80 50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-40. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Vibrational Damping of Ceiling Clips 15
Loudness (Sones)
Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete 10
5
0
0
0.1
0.2
0.3 0.4 0.5 Loss factor of Ceiling Clips
0.6
0.7
0.8
Figure 4-41. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Changing the bending stiffness of the ceiling battens. In this section we see the effect of changing the bending stiffness of the ceiling battens. For reference, the pressed steel battens of Floor 3 had a bending stiffness of about 11000 Nm2. Average Ceiling Surface Vel - Varying Bending Stiffness of Ceiling Battens 80 1375 Nm2 2750 Nm2
Surface Vel rms (dB: re. 5e-8 m/s)
70
5500 Nm2 11000 Nm2 22000 Nm2
60
44000 Nm2 88000 Nm2
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-42. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
Page 107
Average Room Sound Pressure -Varying Bending Stiffness of Ceiling Battens 80 1375 Nm2 2750 Nm2
Sound Pressure (dB: re. 2e-5 Pa)
70
5500 Nm2 11000 Nm2 22000 Nm2
60
44000 Nm2 88000 Nm2
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-43. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Bending Stiffness of Ceiling Battens 14
12
Loudness (Sones)
10
8
6 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
4
2
0
0
1
2
3
4
5
6
7 2
Bending Stiffness of each Ceiling Batten (Nm )
8
9 4
x 10
Figure 4-44. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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4.7
CEILING PROPERTIES
Changing the surface density of the ceiling. In this section the effect of changing the surface density of the ceiling is observed. Only the surface density is changed; we keep the bending stiffness of the ceiling equal to that of 2 layers of 13mm noise control plasterboard. For reference, the surface density of the ceiling of Floor 3 is 25 kg/m2.
Average Ceiling Surface Vel - Varying Surface Density of Ceiling 80 5 kg/m2 10 kg/m2 20 kg/m2 30 kg/m2 40 kg/m2 60 kg/m2 80kg/m2
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-45. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
Page 109
Average Room Sound Pressure -Varying Surface Density of Ceiling 80 5 kg/m2 10 kg/m2 20 kg/m2 30 kg/m2 40 kg/m2 60 kg/m2 80 kg/m2
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-46. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Surface Density of Ceiling 15
Loudness (Sones)
Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete 10
5
0
0
10
20
30
40
50
60
70
80
90
100
2
Surface Density of Ceiling (kg/m )
Figure 4-47. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
Page 110
Changing the bending stiffness of the ceiling. In this section the effect of changing the bending stiffness of the ceiling is observed. Only the bending stiffness is changed; we keep the surface density of the ceiling equal to that of 2 layers of 13mm noise control plasterboard. For reference, the bending stiffness of the ceiling of Floor 3 is 1500 Nm.
Average Ceiling Surface Vel - Varying Bending Stiffness of Ceiling 75 375 Nm, 750 Nm, 1500 Nm, 3000 Nm, 6000 Nm, 12000 Nm
Surface Vel rms (dB: re. 5e-8 m/s)
70 65 60 55 50 45 40 35 30 25
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-48. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Bending Stiffness of Ceiling 80 375 Nm, 750 Nm, 1500 Nm, 3000 Nm, 6000 Nm, 12000 Nm
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-49. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Bending Stiffness of Ceiling 12
Loudness (Sones)
10
8
6 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
4
2
0
0
2000
4000 6000 8000 Bending Stiffness of Ceiling (Nm)
10000
12000
Figure 4-50. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Changing the vibration damping of the ceiling. In this section the effect of changing the vibration damping of the ceiling is observed. For reference, we expect the damping loss factor of the ceiling of Floor 3 to be about 0.02.
Average Ceiling Surface Vel - Varying Damping of Ceiling 80 0.000 , 0.010 , 0.025 , 0.050 , 0.100 , 0.200 , 0.400
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-51. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Damping of Ceiling 80 0.000 , 0.010 , 0.025 , 0.050 , 0.100 , 0.200 , 0.400
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-52. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying the Vibration Damping of Ceiling 12
Loudness (Sones)
10
8
6 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
4
2
0
0
0.05
0.1
0.15 0.2 0.25 Loss factor of Ceiling
0.3
0.35
0.4
Figure 4-53. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Changing the number of layers of plasterboard in the ceiling.
Surface Vel rms (dB: re. 5e-8 m/s)
In the previous sections, where we looked at the ceiling, we changed one parameter and somewhat artificially held other parameters constant. In this section we look at what happens when we increase the number of layers of plasterboard in the ceiling – in effect, we are changing both the surface density and bending stiffness of the ceiling. The noise control plasterboard has a Young’s modulus of 3.7GPa, a thickness of 13mm and a surface density of 12.5 kg/m2 per layer. It is assumed that the layers slip when the ceiling flexes. Average Ceiling Surface Vel - Varying Number of Layers of Plasterboard in Ceiling 80 1 2 3 70 4 5 6 60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-54. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Sound Pressure (dB: re. 2e-5 Pa)
Average Room Sound Pressure -Varying Number of Layers of Plasterboard in Ceiling 80 1 2 70 3 4 5 60 6 50
40
30
20
10
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-55. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Number of Layers of Plasterboard in Ceiling 12 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
Loudness (Sones)
10
8
6
4
2
0
1
1.5
2
2.5
3 3.5 4 Number of layers
4.5
5
5.5
6
Figure 4-56. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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4.8
EFFECTS OF FLOOR SPAN AND ROOM SIZE.
In this section we explore what happens when the dimension of the floor and hence the room change. We look at the floor span, floor width and height of the room. Since the floor dimensions are changing, the performance of the reference concrete floor is recalculated too.
Changing the length of the floor joists. In this section we look at changing the span of the joists, hence the length of the floor and the length of the room.
Average Ceiling Surface Vel - Varying Span of Joists 80 3.000 m, 4.000 m, 5.000 m, 6.000 m, 7.000 m
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-57. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Span of Joists 80 3.000 m, 4.000 m, 5.000 m, 6.000 m, 7.000 m
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-58. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Span of Joists 16 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
14
Loudness (Sones)
12 10 8 6 4 2 0
3
3.5
4
4.5 5 5.5 Span of Floor Joists (m)
6
6.5
7
Figure 4-59. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Changing the width of the floor. In this section we look at changing the width of the floor and hence the width of the room.
Average Ceiling Surface Vel - Varying Width of Floor 80 2.400 m, 3.200 m, 4.000 m, 4.800 m, 5.600 m
Surface Vel rms (dB: re. 5e-8 m/s)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-60. The predicted average ceiling surface velocity normalised against the force of the impact on the floor.
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Average Room Sound Pressure -Varying Width of Floor 80 2.400 m, 3.200 m, 4.000 m, 4.800 m, 5.600 m
Sound Pressure (dB: re. 2e-5 Pa)
70
60
50
40
30
20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-61. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Width of Floor 16 14
Loudness (Sones)
12 10
Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
8 6 4 2 0
2
2.5
3
3.5 4 4.5 Width of Floor (m)
5
5.5
6
Figure 4-62. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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Varying the height of the receiving room. In this section we do not change the floor itself by rather look at changing the height of the receiving room to see how this might affect results. Average Ceiling Surface Vel - Varying Height of Receiving Room 70
Surface Vel rms (dB: re. 5e-8 m/s)
65 60 55 50 45 40 35 30 25
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-63. The predicted average ceiling surface velocity normalised against the force of the impact on the floor. Obviously this does not change with changing receiving room height (unless the room height becomes very small and significantly loads the ceiling vibration). The model, however, does not include such acoustic loading, which is very small for all reasonable floors and room heights.
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Average Room Sound Pressure -Varying Height of Receiving Room 70 2.00 m, 2.20 m, 2.40 m, 2.60 m, 2.90 m
65
Sound Pressure (dB: re. 2e-5 Pa)
60 55 50 45 40 35 30 25 20
0
20
40
60
80 100 120 Frequency (Hz)
140
160
180
200
Figure 4-64. The predicted average room sound pressure generated in the receiving room normalised against the force of the impact on the floor.
Varying Height of Receiving Room 14
12
Loudness (Sones)
10 Footsteps (80kg person) Footsteps 150mm Concrete Japanese Ball Drop Ball Drop 150mm Concrete
8
6
4
2
0
2
2.1
2.2
2.3 2.4 2.5 2.6 2.7 Height of Receiving Room (m)
2.8
2.9
3
Figure 4-65. The average overall Loudness in Sones produced by a model footstep and a Japanese impact ball in the receiving room below the floor.
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4.9
CONCLUSIONS OF THE TREND ANALYSIS.
In this section we offer some conclusions from the prior trend analysis, divided into the floor sections. Joists. • • •
It would appear that increasing the stiffness of the joists substantially improves performance. However, a four-fold increase in bending stiffness is required on the existing joists for a significant gain. Increasing the damping of the joists does improve results by reducing the resonance peaks, especially the fundamental. The addition of transverse stiffeners can show some improvement by increasing the spacing between resonances. The improvement is not very great however, especially for wider floors where much greater transverse stiffness is required to achieve significant results. Such a feature may be best used for very narrow floors.
Floor upper. • • •
It is no surprise that increasing the surface density does improve the performance, but after about 100kg/m2 it would appear that minimal gains are to be had, unless unreasonable surface densities are used. Increasing the bending stiffness of the upper only offers slight gains. Increasing the damping of the upper offers some significant gains in the performance in terms of reducing the resonance peaks. However, the performance as indicated by the loudness of the low-frequency impacts is limited by the first horizontal resonance in the room (along the 5.5m side). In some cases, a resonance in the floor might coincide with that in the room, and in such cases damping would be obviously beneficial.
Floor cavity. •
•
The major conclusion from the floor cavity results is that for cavity depths greater than about 200mm the resilient rubber ceiling clips are the dominant sound transmission path. It is clear that very significant gains could be had by reducing the stiffness of the ceiling clips, or by using independent ceiling joists. However, independent ceiling joists can be prone to flanking transmission issues in a similar way to staggered stud walls. It is interesting to observe the effect increasing the damping of the ceiling clips has on performance. This appears to be due to the fact that, since the ceiling clips are a dominant transmission path, increasing the ceiling clip damping reduces the massspring-mass resonance of the floor system at around 30-40Hz, which in the model tested couples very well into on of the room resonances. We also see an improvement in other low-frequency resonances.
Ceiling. •
Increasing the surface density of the ceiling improves the performance significantly. In fact, doubling the surface density of the ceiling would appear to make the floor perform as well as the reference concrete floor. This result relates well to the fact that airborne sound in double-leafed constructions perform best for a given amount of mass when an equal amount of mass is to be found on each leaf.
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•
Greatly increasing the stiffness of the ceiling can have a detrimental effect whereas increasing the damping has a positive effect. Both of these results are probably related to the fact that the dominant sound path to the ceiling is through the ceiling clips.
Floor and room dimensions. •
• •
Increasing the span of the floor tends to improve performance up to a point. In part, this effect appears to be due to the movement of the fundamental resonance along the longest length of the room to a different frequency which might start to coincide with resonances in the floor. Changing the width of the floor does affect the results, but produces no trend as such, apart from increasing the size of the receiving room and hence the overall sound absorption. Changing the height of the receiving room only changes the results above the first vertical mode of the room (at around 60-80Hz, depending on the height). As a result, there is little influence on the loudness ratings, particularly for footstep sounds, since the energy is mostly concentrated below 80Hz.
4.10 REFERENCES. Blazier, W.E, DuPree, R. B. (1994). “Investigation of low-frequency footfall noise in woodframe, multifamily building construction”, The Journal of the Acoustical Society of America, 96(3), 521-1532 Shi W.; Johansson C.; Sundback U. (1997). An investigation of the characteristics of impact sound sources for impact sound insulation measurement,,Applied Acoustics, 51(1), 85108. Koizumi T. , Tsujiuchi N. , Tanaka H. , Okubo M. , Shinomiya, M. (2002). “Prediction of the vibration in buildings using statistical energy analysis”, http://www.femtools.com/download/docs/imacdu02.pdf
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5 ANALYSIS OF EXPERIMENTAL RESULTS 5.1
INTRODUCTION.
In this chapter we analyse and compare the results obtained from the experimental measurements; primarily from the low-frequency vibration measurements, but also from the standard tapping machine measurements. We first examine the results of the low-frequency vibration measurements, we then briefly look at the tapping machine standard results (the high-frequency results). As part of examining the low-frequency results, we look at illustrative mesh plots for various frequencies on various floors – this provides some interesting insights into what is happening when a floor vibrates under an impact.
5.2
EXAMINATION OF THE LOW-FREQUENCY RESULTS
In this section we look closely at the low-frequency results produced by the shaker and laser vibrometer measurements on the experimental floors. We compare the results of groupings of the floors based on similar themes. For each theme we illustrate the logic behind the inclusion each floor in the test and discuss the results. The following section will then consider the high frequency tapping machine results.
Changing the floor upper of a 7m span floor. We consider floors with 300mm deep LVL joists at 400mm centres spanning 7m. These floors have a plasterboard ceiling consisting of 2 layers of 13mm dense plasterboard (25kg/m2), attached to the joists via rubber ceiling clips (RSIC-1) and a cavity filled with sound control fibreglass batts. We start with a basic floor where the floor upper consists only of 15mm plywood (Floor 2), we then test some additions to this basic floor upper:• The addition of 3 layers of 12.7mm (38mm) of gypsum fibreboard (GIB Sound Barrier 1040kg/m3) screwed to the plywood subfloor. (Floor 3). This addition tests the effect of the addition of mass (40kg/m2) and stiffness to the floor, with a little extra damping provided by the interaction between the layers of gypsum fibreboard. • The addition of 45mm deep battens at 450mm centres perpendicular to the joists with 15mm plywood on the battens; the cavity is infilled with 50mm fibreglass batts (Pink Batts). (Floor 4). This change tests the effect of providing extra stiffness across the floor upper, with a small increase in weight. The cavity is infilled with fibreglass to reduce resonances in the cavity (mostly a higher frequency effect, although this infill will provide some additional damping at lower frequencies too). Similar system to this have been tested by TRADA (Pitts, 2000). • The removal of the fibreglass infill from the above system and the placement of 40mm of paving sand (1250 kg/m3). (Floor 5). The use of sand tests for increasing floor upper mass (and extra mass – 54 kg/m2) with potentially a lot more damping. As explained in the chapter on the overview of existing designs, sand is used in some floor systems in parts of Europe, and can provide significant vibration damping. Results.
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The vibration results (Figure 5-1) show that addition of the upper layers have not changed the position of the fundamental frequency (1st peak), due to the extra stiffness provided by the upper layers compensating for the extra mass. There is a significant movement of the 2nd resonance (2nd peak) due to the increase of the transverse stiffness provided by the additional upper layers. We can see that the extra stiffness transverse to the joists in Floor 4 has help to reduce the size of the peaks in the 1st and 2nd harmonics, and has improved results to about 100Hz, but beyond that there is no real gain (the peak at 118Hz is appears to be caused by resonances of the upper layer of plywood). The extra mass provided by the gypsum fibreboard has improved performance across the whole frequency range. The extra mass and extra stiffness of the sand-filled cavity has improved performance across all frequencies, with significantly extra improvement due to the increased vibration damping showing in frequencies above 80Hz. The predicted sound pressure results (Figure 5-2) show that the 2nd resonances is less important to sound generation, unless it is near a room resonance. Even order plate resonances usually radiate less sound than odd resonances due to more destructive interference of the radiated sound.
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2 √ ceiling, 7 x 3.2m Floor 300mm LVL joists, Fin=1 N at pos C.
80 Basic Floor (#2) 3x GFB (#3) 45mm Fibreglass Batts (#4) 40mm sand (#5)
2 -8 √, dB (re: 5x10 m/s)
70
60
50
40
30
20
20
40
60
80
100 120 Frequency (Hz)
140
160
180
200
2 √ ceiling, 7 x 3.2m Floor 300mm LVL joists, Fin=1 N at pos C.
80 Basic Floor (#2) 3x GFB (#3) 45mm Fibreglass Batts (#4) 40mm sand (#5)
2 -8 √, dB (re: 5x10 m/s)
70
60
50
40
30
20 10
20
30
40 50 Frequency (Hz)
60
70
80
Figure 5-1. Averaged surface velocity plots in dB for Floors 2 to 5 as a function of frequency for the ceiling. The lower graph is a zoomed-in view of the upper graph, looking at very low frequencies. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position C and normalised against the amplitude of the applied force (Fin) for each frequency.
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√ , 7 x 3.2 m Floor, Fin=1 N at pos C. Room 2.5m high α =0.15 80 Basic Floor (#2) 3x GFB (#3) 45mm Fibreglass Batts (#4) 40mm sand (#5)
2 -6 √
, dB (re: 20x10 Pa)
70
60
50
40
30
20
10
20
40
60
80
100 120 Frequency (Hz)
140
160
180
200
Figure 5-2. Averaged sound pressure in dB for Floors 2 to 5 calculated for a room 2.5m high and with a sound absorption coefficient of 0.15 over its surfaces. Generated by the force at position C and normalised against the amplitude of the applied force (Fin).
Improving the vibration damping of the sand. In this section we look at what happens when the damping of the sand-filled cavity is increased by mixing in an amount of sawdust. Mixing in sawdust with the sand increases the vibration damping by reducing the compaction of the sand under its own weight allowing more friction to occur, and by making the impedance of the sand more closely match that of timber. To observe the effect of this we compare two floors where the only difference is the addition of sawdust with the sand. Floor 5 has 40mm of paving sand in the floor, whereas Floor 6 has a mix of 60% sand and 40% sawdust by loose volume (total density of the mix 1170 kg/m3). Results. The vibration and room pressure results (Figure 5-3 and Figure 5-4) show that the addition of sawdust with the sand has significantly increased the damping of the sand. This is apparent in the reduction of levels observed in the frequencies above 80Hz, where modelling has shown damping in the upper surface to play an important part, and where we expect the damping of the sand to be greater. The insignificant change in levels below 80Hz (particularly the 2nd resonance) does suggest that the vibration damping due to the sand is not very much. Sun et al. (1986) observed from experiment that, when looking at sand laid on a vibrating metal plate, the vibration damping in the plate is a maximum at frequencies above when the thickness of the sand is about equal to 0.05λc, where λc is the longitudinal wavelength of the vibrations in the sand ( λc = c f , where c is the propagation speed of the vibrations (100 to 200 m/s for sand) and f is the frequency). In our case, the depth of the sand is 40mm, and if we assume a speed of sound of 150m/s in the sand then the maximum damping is found at 120Hz
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2 √ ceiling, 7 x 3.2m Floor 300mm LVL joists, Fin=1 N at pos C.
80 40mm sand (#5) 40mm sand/sawdust (#6)
2 -8 √, dB (re: 5x10 m/s)
70
60
50
40
30
20
20
40
60
80
100 120 Frequency (Hz)
140
160
180
200
Figure 5-3. Averaged surface velocity plots in dB for Floors 5 and 6 as a function of frequency for the ceiling. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position C and normalised against the amplitude of the applied force (Fin) for each frequency. 2 √
, 7 x 3.2 m Floor, Fin=1 N at pos C. Room 2.5m high α =0.15
80 40mm sand (#5) 40mm sand/sawdust (#6)
2 -6 √
, dB (re: 20x10 Pa)
70
60
50
40
30
20
10
20
40
60
80
100 120 Frequency (Hz)
140
160
180
200
Figure 5-4. Averaged sound pressure in dB for Floors 5 and 6 calculated for a room 2.5m high and with a sound absorption coefficient of 0.15 over its surfaces. Generated by the force at position C and normalised against the amplitude of the applied force (Fin).
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Clamping the ends of the joists. One of the assumptions of the model we used assumes that the joists are simplysupported. That is to say the ends of the joists are in effect resting on a pivot point so that there is little rotational stiffness experienced by the ends of the joists (the ends are not clamped). Work done previously by Scion has shown that in practise it is difficult to clamp the ends of joists (for example, joist hangers essentially simply support the joist ends). What we didn’t know was whether joists in a platform type construction would be clamped by the weight of the remaining building on the joist ends. To find out whether or not there was an effect, we simulated an additional storey on the ends of the joists by clamping the ends of the joists with 2 beams (one on each end) through bottom plates. The beams were stressed so that the force they applied to the ends of the floor was equal to the weight of another storey on the floor. This floor with clamped ends was designated Floor 7. Results. On comparing the results for clamped ends against non-clamped ends (Figure 5-5) we see that there is little difference between the two results. This means that we can continue testing isolated floors with simply-supported joists knowing that the results carry over to floors in buildings. 2 √ ceiling, 7 x 3.2m Floor 300mm LVL joists, Fin=1 N at pos C.
80 40mm sand/sawdust (#6) 40mm sand/sawdust clamped at end (#7)
2 -8 √, dB (re: 5x10 m/s)
70
60
50
40
30
20
20
40
60
80
100 120 Frequency (Hz)
140
160
180
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Figure 5-5. Averaged surface velocity plots in dB for Floors 6 and 7 as a function of frequency for the ceiling. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position C and normalised against the amplitude of the applied force (Fin) for each frequency.
Changing the floor span from 7m to 5.5m. Initially we tested floors with an extreme span of 7m. For subsequent floors we tested a span of 5.5m – a span more likely to be used. In this section we compare two floors which only differ by their span (Floor 6 and Floor 8).
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Results. While, since the forcing points are now on different parts of the floor, we can’t make a meaningful amplitude comparison, we can compare the locations of resonaces. On comparing the low-frequency results for the two different spans (Figure 5-5) we see that the fundamental resonance has increased from 13Hz to 15Hz with a lesser increase for the 2nd resonance. 2 √ ceiling, 3.2m wide Floor 300mm LVL joists, Fin=1 N.
80 40mm sand/sawdust 7m span (#6) 40mm sand/sawdust 5.5m span (#8)
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Figure 5-6. Averaged surface velocity plots in dB for Floors 6 and 8 as a function of frequency for the ceiling. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position C for the 7m floor and position E for the 5.5m floor, and normalised against the amplitude of the applied force (Fin) for each frequency.
Different floor uppers and joists with same cavity depth and 5.5m span. We consider floors with 300mm deep joists at 400mm or 450mm centres spanning 5.5m. These floors have a plasterboard ceiling consisting of 2 layers of 13mm dense plasterboard (25kg/m2), attached to the joists via rubber ceiling clips (RSIC-1) and a cavity filled with sound control fibreglass batts. Two floors have 300mm LVL joists at 400mm centres and two have 300mm I-beams at 450mm centres. We start with Floor 8 which the same as the sand/sawdust cavity-filled Floor 6 but with a shorter span, as a sort off reference floor. We then consider three more floors:• We considered that Floor 8 had some promise but was not good enough to compare well to a 150mm concrete floor. Theoretical results showed that acoustically a floor upper with a surface mass of just over 110kg/m2 can perform significantly better, and that a stiffer floor upper is also useful. Structural analysis also shows that keeping the floor system mass to less than 150kg/m2 requires only normal bracing techniques (particularly for seismic forces). Studies by others have also shown that a deeper layer of sand results in much greater damping at lower frequencies and that floor upper damping is beneficial to performance. With these things in mind we started with Floor
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• •
8 and increased the sand layer to 85mm by replacing the 45mm battens with 90mm deep battens (90 by 45mm timber on edge) in the cavity, we also reduced the amount of sawdust to an 80/20 by loose volume mix (density of sand/sawdust mix is 1210kg/m3). This floor is designated Floor 9. CSR of Australia have a floor design consisting of aerated, autoclaved concrete (Hebel slabs) glued and screwed to 300mm deep I-beam joists at 450mm centres. This floor was tested and is designated Floor 21. In the US and Canada it is common to use a gypsum concrete screed as a topping on a timber subfloor. Current practise and tests by other countries suggest that floating the screed on a resilient layer produces the best results (particularly for higher frequencies). This floating floor screed design was tested with 30mm of USG Levelrock 3500 on 10mm polyurethane foam on a plywood 300mm I-beam subfloor - Floor 22. However, the screed wasn’t laid well and there was significant variation in its thickness.
Results. Looking at the results of the measurements (Figure 5-7 and Figure 5-8) we can see that Floor 9 outperforms all the other floors in this test. The surface density of the floor upper for Floor 9 is 108 kg/m2 and so performs best at lower frequencies. The high damping of the sand/sawdust mix in Floor 9 provides the best performance at higher frequencies too. By comparing the performance of Floor 9 with that of Floor 22 (which has a floor upper surface density of 67 kg/m2), it would seem that the vibration damping of Floor 9 starts becoming quite large at above 60Hz. Comparing the 40mm sand/sawdust Floor 8 (with a floor upper surface density of 48 kg/m2) to the 75mm Hebel slab Floor 21 (52 kg/m2), it would seem that although the floor upper surface is of similar mass the performance of Floor 8 is superior – the extra damping offered by the sand/sawdust mix is beneficial, especially at higher frequencies. It must be remembered, however, that the LVL joists used in Floor 8 give an extra 12kg/m2 of mass to the floor over the I-beams used in Floor 21. It is interesting to note that although the floating screed is designed to provide improved impact insulation at higher frequencies due to it floating on a very resilient foam layer, the sand/sawdust floors are able to provide a similar or much better higher frequency performance. This is even though the top layer of plywood of the sand/sawdust is directly connected to the subfloor without any floating arrangements. This shows the effectiveness of the sand in damping the vibrational energy.
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2 √ ceiling, 5.5 x 3.2m Floor, Fin=1 N at pos E.
80 40mm sand/sawdust (#8) 85mm sand/sawdust (#9) 75mm Hebel (#21) Levelrock (#22)
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2 √ ceiling, 5.5 x 3.2m Floor, Fin=1 N at pos E.
80 40mm sand/sawdust (#8) 85mm sand/sawdust (#9) 75mm Hebel (#21) Levelrock (#22)
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Figure 5-7. Averaged surface velocity plots in dB for Floors 8,9,21 and 22 as a function of frequency for the ceiling. The lower graph is a zoomed-in view of the upper graph, looking at very low frequencies. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position E and normalised against the amplitude of the applied force (Fin) for each frequency.
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2 √
, 5.5 x 3.2 m Floor, Fin=1 N at pos E. Room 2.5m high α =0.15
80 40mm sand/sawdust (#8) 85mm sand/sawdust (#9) 75mm Hebel (#21) Levelrock (#22)
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Figure 5-8. Averaged sound pressure in dB for Floors 8,9,21 and 22 calculated for a room 2.5m high and with a sound absorption coefficient of 0.15 over its surfaces. Generated by the force at position E and normalised against the amplitude of the applied force (Fin).
Transverse stiffening. It was thought that one way to improve the low-frequency performance was to reduce the number of resonances occurring in the very low frequency region. Now since a lot of the resonances occurring in the very low frequency region are due to the floor bending in the direction perpendicular to the joists (as can be seen in section 5.4), one way to achieve that aim would be to greatly stiffen the floor in the direction perpendicular to the joists. Such stiffening has been dubbed ‘transverse stiffening’, and can be achieved by introducing blocking or sections of joists which fit between the floor joists. Each block needs to be connected to the neighbouring block to enable rotational moments to be transmitted, one way to do this is to clamp the blocks or joist sections together using tie rods. One problem to avoid with the addition of transverse stiffeners is making the fundamental frequency of the floor becoming higher in frequency making the human hearing more sensitive to the sound. If the width of the floor is relatively narrow, the addition of transverse stiffeners may make the fundamental resonance more audible (unless its amplitude is correspondingly reduced). To reduce this issue and to make the installation of transverse stiffeners easier, it was thought that the blocking which constituted the transverse stiffeners would not be installed between the floor edge and the next joist (See diagrams and photographs of Floor 12 and Floor 15 to illustrate this. One problem with this is that we now have introduced a rotational mode in the floor, whose frequency depends on the bending stiffness of the floor upper. However, since it is an even type mode the sound radiation efficiency would be quite low.
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Results. In Figure 5-9 we see the results of introducing transverse stiffeners into a floor which consists of plywood on joists without a ceiling (Floor 10). We can see that inclusion of the transverse stiffeners has not changed the fundamental resonance (at 23Hz), and the transverse resonances which occurred up to about 60Hz have been eliminated or reduced. We also see, however, that another mode (at 27.5Hz, and illustrated in section 5.4) has been added; this is a rotational mode. We see that for this width and length of floor (3.2 m and 5.5m respectively) the use of 2 transverse stiffeners (in Floor 13) is about a good as 4 (in Floor 12). One of the hoped for advantages of including transverse stiffeners in a floor is to produce a floor which is light in weight. Floor 14 is the same as Floor 13 expect a ceiling has been added. In Figure 5-10 we compare the low-frequency performance of Floor 14 against a floor with some extra mass and stiffness in the floor upper – 75mm Hebel slab (Floor 21). We observe a similar performance at frequencies below 100Hz, but an apparently poorer performance for frequencies above 100Hz. Transverse stiffeners made from I-beam sections were added to the Hebel floor (Floor 20) to observe whether they would improve performance for such a floor. While there is some increase in the fundamental and 2nd order resonance, the overall result is much the same, showing that there is no point in adding transverse stiffeners to a floor with an already significantly built up upper. And, while there appears to be some benefit to using transverse stiffening to improve very low frequency performance for floors with thin uppers, it is probably not enough for what we need. Another issue with transverse stiffeners, which is illustrated in the theoretical analysis chapter, is that the wider the floor becomes the more transverse stiffening you need to provide effective shifting of the resonances. 2 √ upper, 5.5 x 3.2m Floor, Fin=1 N at pos E.
100 Basic Floor (#10) 4 Transverse Stiffeners (#12) 2 Transverse Stiffeners (#13)
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Figure 5-9. Averaged surface velocity plots in dB for Floors 10, 12 and 13 as a function of frequency for the floor upper surface. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position E and normalised against the amplitude of the applied force (Fin) for each frequency.
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2 √ ceiling, 5.5 x 3.2m Floor, Fin=1 N at pos E.
80 2 Transverse Stiffeners (#14) 75mm Hebel + 2 Trans Stiffeners (#20) 75mm Hebel (#21)
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2 √ ceiling, 5.5 x 3.2m Floor, Fin=1 N at pos E.
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Figure 5-10. Averaged surface velocity plots in dB for Floors 14, 20 and 21 as a function of frequency for the ceiling. The lower graph is a zoomed-in view of the upper graph, looking at very low frequencies. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position E and normalised against the amplitude of the applied force (Fin) for each frequency.
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2 √
, 5.5 x 3.2 m Floor, Fin=1 N at pos E. Room 2.5m high α =0.15
80 2 Transverse Stiffeners (#14) 75mm Hebel + 2 Trans Stiffeners (#20) 75mm Hebel (#21)
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Figure 5-11. Averaged sound pressure in dB for Floors 14, 20 and 21 calculated for a room 2.5m high and with a sound absorption coefficient of 0.15 over its surfaces. Generated by the force at position E and normalised against the amplitude of the applied force (Fin).
Comparing a deeper cavity against more mass in the floor upper. Measurements were made on a floor consisting of 400mm deep I-beams at 600mm centres spanning 5.5m with 20mm particleboard as the floor upper (Floor 18), and a floor consisting of 300mm deep I-beams at 450mm centres spanning 5.5m with 75mm Hebel aerated concrete as the floor upper (Floor 18). The ceiling and ceiling fixing details were the same for both floors. By comparing the results of these floors we can observe differences in performance a deeper cavity makes against a floor with greater mass in the floor upper. Results. Looking at Figure 5-12 we can see that the fundamental frequency of Floor 18 is greater than that of Floor 21 indicating a stiffer and lighter floor. Overall, however, we can see that Floor 21 tends to perform better.
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2 √ ceiling, 3.2m wide Floor, Fin=1 N
80 400mm I-beams (#18) 300mm I-beams + 75mm Hebel (#21)
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Figure 5-12. Averaged surface velocity plots in dB for Floors 2 and 18 as a function of frequency for the ceiling. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position C (for Floor 2) and E (for Floor 18) and normalised against the amplitude of the applied force (Fin) for each frequency.
Adding mass to the ceiling. Instead of adding mass to the floor upper it is possible (but possibly less convenient) to add mass to the ceiling. This was tested out on Floor 18 by adding another two layers of 13mm noise control plasterboard giving the ceiling 50kg/m2 of mass, letting everything else remain the same, to produce Floor 19. Results. Figure 5-13 and Figure 5-14 show the results of the measurements of Floors 18 and 19. We see that the doubling of the ceiling mass does reduce the vibration levels of the ceiling by up to 5dB, but this doesn’t always correspond to the same changes in the predicted sound pressure levels, as is often the case since changing the properties of the radiating surface changes the bending wavespeed and hence its radiation efficiency.
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√ ceiling, 5.5 x 3.2m Floor, Fin=1 N at pos E. 80 400mm I-beams (#18) 400mm I-beams + 2x ceiling mass (#19)
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Figure 5-13. Averaged surface velocity plots in dB for Floors 18 and 19 as a function of frequency for the ceiling. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position E and normalised against the amplitude of the applied force (Fin) for each frequency.
√ , 5.5 x 3.2 m Floor, Fin=1 N at pos E. Room 2.5m high α =0.15 80 400mm I-beam joists (#18) 400mm I-beam joists 4x13mm plasterb (#19)
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Figure 5-14. Averaged sound pressure in dB for Floors 18 and 19 calculated for a room 2.5m high and with a sound absorption coefficient of 0.15 over its surfaces. Generated by the force at position E and normalised against the amplitude of the applied force (Fin).
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Independent ceiling joists. The theoretical modelling of the floor systems showed that the ceiling clips (RSIC-1) used to resiliently attach the ceiling to the joists were the major sound transmission path for a cavity depth of about 200mm or greater. One way to overcome this problem is to remove the ceiling clips by using independent ceiling joists. To test the effectiveness of using independent ceiling joists the resiliently attached ceiling of the gypsum concrete floor system (Floor 22) was removed and replaced with a ceiling supported by way of a independent ceiling joist system (Floor 23). It was know that one of the problems that can occur with such a independent ceiling joist system is that flanking transmission of vibration around the edge of the floor can be a compromising factor. To reduce such flanking the ends of the ceiling joists were mounted on rubber pads and the ceiling perimeter, including the battens, was cut with a 10mm gap so that it didn’t touch the wall. Results. Figure 5-15 and Figure 5-16 show the results of the measurements comparing the resiliently attached ceiling to the ceiling attached to independent ceiling joists. It is cleat that there is little difference between the resilient attached ceiling and the ceiling with independent ceiling joists with no special anti-flanking treatment (Floor 22 cf. Floor 23). However, once we include special treatment to reduce flanking issues, we observe a significant decrease in the ceiling vibration levels, which is in line with theoretical observations. 2 √ ceiling, 5.5 x 3.2m Floor, Fin=1 N at pos E.
80 Gypsum Conc - RSIC clips (#22) Gypsum Conc - Independent ceil joists (#23) Gypsum Conc - Isolated ceil joists (#24)
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Figure 5-15. Averaged surface velocity plots in dB for Floors 22 to 24 as a function of frequency for the ceiling. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position E and normalised against the amplitude of the applied force (Fin) for each frequency.
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2 √
, 5.5 x 3.2 m Floor, Fin=1 N at pos E. Room 2.5m high α =0.15
70 Gypsum Conc - RSIC clips (#22) Gypsum Conc - Independent ceil joists (#23) Gypsum Conc - Isolated ceil joists (#24)
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Figure 5-16. Averaged sound pressure in dB for Floors 22 to 24 calculated for a room 2.5m high and with a sound absorption coefficient of 0.15 over its surfaces. Generated by the force at position E and normalised against the amplitude of the applied force (Fin).
Final Floor Designs. Subjective analysis of sounds recorded from Floor 9 showed that the overall performance of this floor was similar to that of a 150mm concrete slab floor with a suspended ceiling (the concrete floor being designated Floor 0). We can therefore regard this floor design (Floor 9) as being an effective floor design. If we regard the performance of this timber floor as being a suitable standard for timber floors, we can compare the performance of other potential final floor designs. Using the learning gained from the theoretical and experimental analysis, another final floor design built and tested was Floor 25. This floor combines the ideas of using mass and damping in the form of a sand/sawdust mix in the floor upper, but with a reduced amount to decrease overall weight, and to make the floor less deep. The proposed amount of sand/sawdust mix to use was 65mm (in a cavity 70mm deep). However, after the measurements it was discovered that the builders did not fill the cavity to 65mm, but rather filled the cavities to about 50mm on average. Although not ideal, this may be regarded as a test of buildability. The reduction of sand and sawdust in the floor upper was offset by using independent ceiling joists mounted on rubber pads. The edges of the ceiling were not firmly mechanically connected to the wall, but were sealed with a bead of acoustic sealant, which provides a resilient connection between the edge of the ceiling and the wall. In one measurement coving was used to cover this resilient connection, to test the effect of such a detail on this flanking sensitive design. Results. Figure 5-17 shows the ceiling surface vibration results for the Floor 9 and Floor 25; in the same figure we also compare Floor 2 – the ‘basic’ floor. Figure 5-18 shows the predicted sound pressure levels for Floors 9 and 25 – we don’t compare with Floor 2, since that floor and Page 141
hence room is a different size. We see that Floor 25 performs about as well as Floor 9 up to 100Hz, beyond that, however, Floor 25’s performance is slightly worse than Floor 9 (about 4dB, on average). However, when considering soft-shoe footsteps of an 80kg person walking, and after factoring in the threshold of hearing from 100Hz to 200Hz, we find that the frequencies from 100Hz to 200Hz would still be inaudible for footsteps on Floor 25. Therefore, it can be concluded that Floor 25 performs similarly to Floor 9 in the low-frequency range. Figure 5-19 shows the effect the coving has on the performance. It does seem that the coving has indeed affected the performance of the system, particularly above 60Hz. 2 √ ceiling, 3.2m wide Floor, Fin=1 N.
80 Basic Floor (#2) 85mm sand/sawdust (#9) 65mm sand/sawdust + independent ceil joists (#25)
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Figure 5-17. Averaged surface velocity plots in dB for Floors 2, 9 and 25 as a function of frequency for the ceiling. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position C (for the Floor 2) and E (for Floors 9 and 25) and normalised against the amplitude of the applied force (Fin) for each frequency. The spike at 150Hz is due to electrical interference of the measurement process.
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2 √
, 3.2 m wide floor, Fin=1 N. Room 2.5m high α =0.15
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Figure 5-18. Averaged sound pressure in dB for Floors 2, 9 and 25 calculated for a room 2.5m high and with a sound absorption coefficient of 0.15 over its surfaces. Generated by the force at position E and normalised against the amplitude of the applied force (Fin). 2 √ ceiling, 3.2m wide Floor, Fin=1 N.
80 65mm sand/sawdust + independent ceil joists (#25) Floor 25 with ceiling perimeter coving (#26)
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Figure 5-19. Averaged surface velocity plots in dB for Floors 25 and 26 as a function of frequency for the ceiling. The surface velocity is measured by the scanning laser vibrometer, with force generated by the shaker at position E and normalised against the amplitude of the applied force (Fin) for each frequency. The spike at 150Hz is due to electrical interference of the measurement process.
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5.3
EXAMINATION OF THE HIGH-FREQUENCY RESULTS.
In this section we consider the impact insulation results produced by the standard tapping machine on the bare floors (that is without any additional covering). We do this by looking at the overall Ln,w rating each floor achieved as a result. We used the relevant part of ISO 140 for the test and the single figure ratings are produce in accordance with ISO 717-2. We also include IIC ratings (in accordance with ASTM E989) and spectrum adaptation terms to give Ln,w + CI, although Ln,w + CI tends to have mid-frequency emphasis. We only have these results for floors that had ceilings or complete ceilings. The worst performing floors for high-frequency impact insulation as indicated by a high Ln,w rating are Floor 0 (the 150mm concrete slab), Floor 21 and 22 (the floors with 75mm aerated concrete slabs on top). Although these floors would meet the Australian building code requirements ( Ln,w + CI ≤ 62 ), they would not nearly meet the New Zealand building code requirements (IIC ≥ 55), and would require an additional soft surface covering to perform. This is due to their hard upper surfaces with very little damping in the floor upper. Floor 23 (the gypsum concrete floor) also has a hard surface, but to compensate for this, the floor is floating on a resilient foam layer, this results in good high-frequency performance. We also note that when we compare the resiliently attached ceiling (Floor 22) with the ceiling using independent ceiling joists without any special anti-flanking treatment (Floor 23), we get the same result. This suggests that we can use independent ceiling joists to replace the use of RSIC ceiling clips. The other floors of plywood, particleboard and gypsum fibreboard tended to have a softer upper surface, resulting in less generation of impact vibration in the floor structure. Their high frequency performance tends, as a result to be better. The basic floor (Floor 2) as a result has a much better rating for Ln,w, although because of its lesser mass the mid-frequencies range performance is not so good and Ln,w + CI rating is not that good. The extra layer of plywood on battens (in Floor 4) has improved the high frequency performance over Floor 2. However the biggest gains are to be had by the floors with a more massive upper with extra damping in the upper (Floors 3, 5, 6, 7, 8, 9 and 25). Comparing Floor 18 with 19 we see that the extra ceiling layers did nothing to improve the high-frequency performance. Comparing Floor 6 with 8 we see that changing the span of the floor makes no real difference to the results. Comparing Floor 18 with 2 we see that a deeper floor, the use of I-beams with a greater spacing improves the high frequency impact insulation performance. Comparing Floor 25 with 26 we see that the addition of coving around the perimeter of the ceiling has caused problems resulting in a drop in performance. We do, however, find that the addition of transverse stiffeners (Floor 14 cf. Floor 2) does seem to improve the high frequency performance quite significantly. However, the transverse stiffeners in Floor 20 seemed to offer no change. The best performing floors for the high-frequency ratings are Floor 3, Floor 9 and Floor 25. We expect Floor 9 and Floor 25 to perform well because of their high mass and damping and, in the case of Floor 25, the isolated ceiling (However the addition of coving . Floor 3 performs well possibly because it upper surface consists of gypsum fibreboard, which seems to be softer than plywood and particleboard. Floor 3 also has some significant damping due to the interaction of the layers gypsum fibreboard as well as due to the extra mass of the gypsum fibreboard.
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Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor Floor
0 2 3 4 5 6 7 8 9 14 18 19 20 21 22 23 25 26
IIC
Ln,w
CI
Ln,w+CI
37 49 61 53 57 58 58 59 62 55 52 51 35 35 58 58 62 60
69 61 45 58 52 52 52 51 48 56 58 59 71 72 52 53 48 50
-12 -1 1 -1 0 -1 -1 -1 -2 0 0 0 -9 -10 -2 -2 -2 -1
57 60 46 57 52 51 51 50 46 56 58 59 62 62 50 51 46 49
Table 5-1. The standard single figure ratings of the tapping machine results for the tested floors without any floor covering (bare floor).
5.4
BRIEF EXAMINATION OF THE VIBRATION WAVEFORMS OBSERVED.
One of the important results of doing vibration measurements on the test floors, as was done for this project, is that we can see the shapes of vibrations which are being produced this enables us to identify the modes which are producing resonances and to have a deeper understanding of what is happening in a floor. This is particularly useful for developing a theoretical model of such floors. In this section we examine a few mesh plots of the results of the measurements of some floors to illustrate a few features found in the vibration of floors. Obviously the data produced by such was enormous and we can only hope to pick a few points in the hope that they will be illuminating. Simple floor – panel on solid joists. We start with examining floor 10 as it is simply 15mm plywood screwed to 300mm deep LVL joists spanning 5.5m and which are spaced at 400mm centres. It has no ceiling.
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2 √ , 5.5 x 3.2 m Floor 10 Upper, Fin=1 N at pos E.
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Figure 5-20. Averaged surface velocity plot in dB for Floor 2 as a function of frequency for the upper part of the floor (there is no ceiling). As measured by the scanning laser vibrometer, generated by the force at position E and normalised against the amplitude of the applied force (Fin) for each frequency.
Referring to Figure 5-20,we see that there are clear peaks at 21 to 23Hz, these correspond to the fundamental (1,1) and second modes (1,2) of the floor and are shown in Figure 5-21 and Figure 5-22, but since they are close together, their shapes are not very distinct. The next peak is at 40Hz, this corresponds to the fourth mode (1,4) and is shown in Figure 5-23. The third mode is not clearly observed for this floor under the applied force. The next clear mode (1,5) is at 50Hz as shown in Figure 5-24. Similarly, modes (1,6) and (1,7) are at 55Hz and 65Hz, respectively. The first mode where we see more bending along the joists is at 74Hz; this is mode (2,2), and is shown in Figure 5-25. We would also expect to see mode (2,1), but this is not apparent, and may be very close to mode (2,2). From 74Hz we see a number of peaks in the response which correspond to higher floor modes, e.g. mode (2,5) is at 90Hz and is shown in Figure 5-26. Above 100Hz we find that the modes don’t form clear peaks anymore. They tend to become close together and the average surface velocity tends to be dominated by vibration near the excitation point, as illustrated by the response at 155Hz, Figure 5-27. The above observations suggest that this simple floor behaves, at very low-frequencies below about 100Hz, like a plate with orthotropic stiffness – the joists are firmly connected to the plywood. At frequencies above 100Hz the wavelengths of the vibrations on the plywood become shorter than you might expect if the plywood was attached firmly to the joists. This suggests that the plywood is starting to separate from the joists at regions between screws.
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Displacement per unit force at 22Hz, and at phase 90° relative to force
-6
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Figure 5-21. Illustration of mode (1,1) on floor 10.
Displacement per unit force at 23Hz, and at phase 0° relative to force
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-4 -1
-0.5
-5 y (m)
x (m)
Figure 5-22. Illustration of mode (1,2) on floor 10. Note that the phase with respect to the force is 0 in this illustration. This illustrates the reactionary vibration near the forcing point. It is not apparent for a phase of 90 degreees. Page 147
Displacement per unit force at 40Hz, and at phase 90° relative to force
-6
Vertical displacement (m)
x 10
1 0.5 0 -0.5
-1 -2
-1 -3 -3
-4
-2
-1
-5
x (m)
y (m)
Figure 5-23. Illustration of mode (1,4) on floor 10. Displacement per unit force at 50Hz, and at phase 90° relative to force
-6
Vertical displacement (m)
x 10 1 0.5 0
-1 -2
-0.5 -3
-1 -3
-4 -2
-5
-1
y (m)
x (m)
Figure 5-24. Illustration of mode (1,5) on floor 10.
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Displacement per unit force at 74Hz, and at phase 90° relative to force
-6
Vertical displacement (m)
x 10
1
0
-1
-1 -2 -3
-3
-4
-2 -1
-5
x (m)
y (m)
Figure 5-25. Illustration of mode (2,2) on floor 10. Displacement per unit force at 90Hz, and at phase 90° relative to force
-6
Vertical displacement (m)
x 10
1 0
-1 -2
-1 -3 -3
-4
-2 -1
-5
x (m)
y (m)
Figure 5-26. Illustration of mode (2,5) on floor 10.
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Displacement per unit force at 155Hz, and at phase 90° relative to force
-6
Vertical displacement (m)
x 10
5 0 -1
-5 -2 -3 -3
-4
-2 -1
-5
x (m)
y (m)
Figure 5-27. Illustration of response at 155Hz on floor 10. The region near the forcing point is showing a lot of reactionary movement (vibration which doesn’t send energy into the structure, but oscillates the energy back and forth between the forcing device and the floor).
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Basic floor with ceiling. The next floor to consider is floor 2. This is a basic floor with a ceiling, consisting of two layers of plasterboard screwed to ceiling battens connected to the underside of the joists through resilient rubber clips (RSICs). The cavity is infilled between the joists with a 300mm depth of fibreglass batts (flow resistivity = 7200 Rayls/m). The overall cavity depth is 340mm. This floor spans 7m. We will examine some 3D mesh plots of the vibrations on the surfaces of this floor to illustrate some points to do with coupling of the vibrations of the upper part of the floor to the ceiling vibrations. We observe that for modes (1,1) and (1,2) at 13Hz and 20Hz respectively, the ceiling is closely coupled to the upper part of the floor. This is illustrated in Figure 5-29, for mode (1,2). We also see that at 32Hz the ceiling is starting to decouple from the floor upper (see Figure 5-30). The coupling of the ceiling to the floor upper is through the air and the ceiling clips under the joists. The frequency above which this decoupling occurs is related to the mass and coupling stiffnesses of the floor/ceiling system. This is called the mass-stiffnessmass resonance frequency, and assuming the floor upper and ceiling has no bending stiffness (totally limp) and the cavity has no infill, is given by 1/ 2
m + m2 , f = 2π k 1 (5-26) m m 1 2 where m1 is the surface density of the floor upper, m2 is the surface density of the ceiling, and k is the stiffness coupling the two together. k is given by ρ c2 k = 0 + k clips , (5-27) d where ρ0 is the density of air, c is the speed of sound in the air, d is the cavity depth, kclips is the average stiffness of the ceiling clips per unit area. For the case of Floor 2 using the above assumptions we find that the mass-stiffness-mass resonance frequency is 39Hz. A rough approximation since our floor and ceiling clearly are not limp. In the vibration response of the ceiling we see that there frequencies where we get peaks. This is most probably due to the situation where we have floor resonances coupling well into ceiling resonances. This is illustrated for a range of peaks in Figure 5-31, Figure 5-32 and Figure 5-33. Since it would appear that resonance are occurring in the ceiling, this would suggest that a lot of the vibration in the ceiling is being transmitted by point source coupling, presumably through the ceiling clips.
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2 √ , 7 x 3.2 m Floor 2 ceiling, Fin=1 N at pos C.
80
2 -8 √, dB (re: 5x10 m/s)
70
60
50
40
30
20
20
40
60
80
100 120 Frequency (Hz)
140
160
180
200
Figure 5-28. Averaged surface velocity plots in dB for Floor 2 as a function of frequency for the ceiling. As measured by the scanning laser vibrometer, generated by the force at position C and normalised against the amplitude of the applied force (Fin) for each frequency.
Displacement per unit force at 20Hz, and at phase 90° relative to force
-6
Vertical displacement (m)
x 10
6 4 2 0 -2 -1
-4
-2
-6
-3 -4 -3
-2
-5 -1
-6 y (m)
x (m)
Figure 5-29. Illustration of vibration response of upper surface and ceiling at 20Hz on floor 2. This is mode (1,2). At this frequency the ceiling is clearly closely coupled to the floor upper surface.
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Displacement per unit force at 32Hz, and at phase 90° relative to force
-6
Vertical displacement (m)
x 10
1 0.5 0 -0.5
-1 -2
-1
-3 -4 -5
-3
-2
-1
-6 y (m)
x (m)
Figure 5-30. Illustration of vibration response of upper surface and ceiling at 32Hz on floor 2. This is mode (1,4). At this frequency the ceiling is starting to decouple from the floor upper surface, and produce modes of its own. Displacement per unit force at 56.5Hz, and at phase 0° relative to force
-7
x 10
Vertical displacement (m)
6 4 2 0 -2
-1 -2
-4
-3
-6
-4 -3
-5 -2
-1
-6 y (m)
x (m)
Figure 5-31. Illustration of vibration response of upper surface and ceiling at 56.5Hz on floor 2. At this frequency the ceiling is quite decoupled from the floor upper surface, and appears to be resonating. This is a peak in the response of the system, probably due to a resonance in the upper floor coupling to a resonance in the ceiling, Page 153
Displacement per unit force at 56.5Hz, and at phase 0° relative to force
-7
x 10
Vertical displacement (m)
6 4 2 0 -2
-1 -2
-4
-3
-6
-4 -5
-3
-2
-1
-6 y (m)
x (m)
Figure 5-32. Illustration of vibration response of upper surface and ceiling at 75Hz on floor 2. This is another peak in the response of the system, and is also probably due to a resonance in the upper floor coupling to a resonance in the ceiling, Displacement per unit force at 165Hz, and at phase 90° relative to force
-7
Vertical displacement (m)
x 10
3 2 1 0 -1 -1
-2 -2
-3
-3 -4 -3
-5 -2
-1
-6 y (m)
x (m)
Figure 5-33. Illustration of vibration response of upper surface and ceiling at 165Hz on floor 2. This is at another peak in the response of the system, and is also probably due to a resonance –mode (4,5) – in the upper floor coupling to a resonance in the ceiling. The vibrations in the upper floor die away quite quickly due to the coupling of energy into the ceiling. Page 154
A floor with a thick, stiff upper surface. In this section we examine a few plots from Floor 21, which consists of 75mm of Hebel aerated concrete screwed to I-beam joists. In Figure 5-34 we see the measurements results of the floor at 190Hz. What is clear from the relatively long wavelengths at this frequency is the floor upper is quite stiff in all directions. We also see that the waves in the floor upper do not die away at all, indicating very low damping in the floor upper.
Displacement per unit force at 190Hz, and at phase 90° relative to force
-8
Vertical displacement (m)
x 10
5
0
-5 -1 -2 -3
-3 -2
-1
-4 -5
x (m)
y (m)
Figure 5-34. Illustration of vibration response of upper surface and ceiling at 190Hz on Floor 21. This is at another peak in the response of the system, and is also probably due to a resonance –mode (6,5) – in the upper floor coupling to a resonance in the ceiling.
A floor with more mass and high damping. In Figure 5-35 we see the effect on the vibrations in the floor upper when we have a floor which is highly damped (Floor 9). We observe that the vibrations are quickly damped by the floor upper, resulting in a relatively quick reduction in their amplitude as they travel along the floor. This means that less vibration is transmitted to the ceiling as a whole; it also means that in such a floor flanking is less of an issue, since less vibrational energy gets to the rest of the structure.
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Displacement per unit force at 190Hz, and at phase 90° relative to force
-7
x 10
Vertical displacement (m)
1.5 1 0.5 0 -0.5 -1
-1
-1.5
-2 -3 -3
-2.5
-2
-4 -1.5
-1
-0.5
-5 y (m)
x (m)
Figure 5-35. Illustration of vibration response of upper surface and ceiling at 190Hz on floor 9. The vibrations in the upper floor die away quite quickly due to the energy lost by the internal damping of the floor upper.
A floor with transverse stiffeners. In Floor 14 we considered the case of having transverse stiffeners in a relatively simple floor. It was said before that one concern was not to increase the frequency of the fundamental resonance, as it is believed that this would make it more audible to listeners. One way around that problem was to provide a gap between the end of the transverse stiffener and the edge of the floor. This, however, resulted in an additional rotational mode. This mode (at 25Hz) is shown in Figure 5-36.
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Displacement per unit force at 25Hz, and at phase 90° relative to force
-6
x 10
Vertical displacement (m)
1.5 1 0.5 0 -0.5 -1
-1 -2
-1.5
-3 -3
-4 -2.5
-2
-1.5
-1
-0.5
x (m)
-5 y (m)
Figure 5-36. Illustration of vibration response of upper surface and ceiling at 25Hz on floor 14. This is an illustration of the rotational mode found in the floor, due to the transverse stiffeners not going completely to the wall.
A floor with a floating topping. In this example we consider Floor 22, which has a gypsum concrete screed floating on a foam layer on the floor. The gypsum concrete is relatively stiff and heavy and the function of the foam is to isolate the vibrations of the screed from the rest of the floor. This is more effective at higher frequencies. In Figure 5-37 we can see that this is happening – the gypsum concrete is vibrating with little damping occurring, with the edges obviously being free to move.
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Displacement per unit force at 190Hz, and at phase 0° relative to force
-8
x 10
Vertical displacement (m)
6 4 2 0 -2 -1
-4 -2 -3
-6 -3
-2.5
-4 -2
-1.5
-1
-0.5
x (m)
-5 y (m)
Figure 5-37. Illustration of vibration response of upper surface and ceiling at 190Hz on floor 22. This is an illustration of what happens when we have a floating topping.
5.5
REFERENCES.
Pitts, G. (2000). Acoustic Performance of party floors and walls in timber framed buildings, TRADA Technology report 1/2000. Sun, J.C., Sun, H.B., Chow, L.C., Richards, E.J. (1986). “Predictions of total loss factors of structures, part II: Loss factors of sand-filled structure”, Journal of Sound and Vibration, 104(2), 243-257.
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6 SUBJECTIVE LISTENING TESTS AND ASSESSMENTS
6.1
INTRODUCTION
Subjective listening tests were carried out to determine the acceptability of the various timber joist floor/ceiling designs in comparison with a standard concrete floor/ceiling system. The tests were designed to focus particularly on the domestic environment because that is not only the most relevant but also is likely to be the most critical environment. The reason is that the insulation required in dwellings is not based on short-term tolerance or, merely, an adequate freedom from interruption of one’s enjoyment of TV (or other restricted, defined activity) but a need to provide acoustic privacy. In the extreme case acoustic privacy may be defined as the state whereby no information about you or your neighbours (including your or their presence) is communicated by sound. We can expect that, as with other human characteristics such as hearing acuity and noise sensitivity, the need for acoustic privacy will exhibit a range within the population. Our knowledge of the form and extent of the distribution of this facet of human character is, at this stage, very limited so we have included - as part of the subjective tests - questionnaires which aim to quantify each subject’s need for acoustic privacy and their intrinsic sensitivity to noise (not to be confused with hearing acuity!) Floor/ceiling structures would be ideal if, when supporting normal activities (walking, children’s play, objects being dropped, loudspeaker use etc), they produce no audible indications of these activities to occupants of adjacent rooms. Trends in modern living can be seen as likely to increase the insulation needed to achieve this. More and more of our population are living in apartments and town houses, and home entertainment systems capable of unprecedented power at bass frequencies are now commonplace. Current fashion encourages the use of these systems at high levels. The loudspeakers of these systems are often in direct contact with the floor and therefore efficiently couple their vibrations into the building structure. We may also observe that contemporary society is becoming more individualistic and egocentric, therefore we can expect less constraint on noisy behaviour mediated by a sense of what might impact on a neighbour. Surveys (see, for example, Grimwood and van Dongen) confirm that typical floor/ceiling systems usually do allow neighbours to hear the activities they support, although this may be undetected during times when there is sufficient ambient noise to mask the sound. Clearly such floors are not 100% satisfactory – and this is especially the case during the evening and night when external activity noise tends to diminish markedly. The common interpretation of acoustic privacy, unintentionally supports this unsatisfactory position. Acoustic privacy is usually cited as a necessary requirement for dwellings but instead of this being seen as a need to protect users from invasion of their privacy by audible evidence of the uninvited presence of others (i.e. by incoming sound from their activities), it is interpreted simply as a need to provide speech confidentiality. Speech confidentiality can be
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achieved with little or no impediment to structure borne sound and in these cases attenuation of floor impact noise is unlikely to be sufficient to provide privacy. The ultimate aim of research on the insulation provided by floor-ceiling systems must be to determine what is required to render impact noises completely non problematic. In this project we have addressed an interim goal of demonstrating that LTF based floor-ceiling constructions can be designed to match, or exceed, the insulation achieved by a concrete-based floor (interpreted as 150 mm slab with a plasterboard suspended ceiling). Because of the restricted time available and a need to make the listening task not too onerous for subjects, the testing was intentionally limited, but a second stage of listening assessments and data mining is planned after a more complete paired-comparison experiment. 6.2
SUBJECTIVE VERSUS OBJECTIVE TESTING
International and national standards bodies prescribe methods (e.g. ISO 140, ASTM E99, JIS A 1418) for assessing the relative performance of floor systems based on objective measurements. But since the present project arose because of occupant dissatisfaction with the subjective perception of the performance of LTF structures, this indicates that either the established methods of quantifying impact sounds or the acceptability criteria based on them, are inadequate. In this project we needed to demonstrate that our proposals for improved timber-based structures will attenuate impact sounds to the satisfaction of listeners to at least the same extent as the reference concrete structure, and secondly we wanted to establish what objective measures are required to ensure this equivalence of performance. Our approach, therefore, involved (1) making standard objective measurements, and (2) collecting recordings of sounds from realistic impact sources of impacts on the floors which were then replayed to listeners for comparison and assessment. The objective measures consisted of the standard normalised impact sound pressure level using the ISO standard tapping machine (in accordance with ISO 140-IV) both on the concrete slab in the ARC which is – as far as can be ascertained - within a few mm (≤ 10 mm) of the 150 mm target (with a plasterboard suspended ceiling underneath), and the complete range of LTF experimental floors built into the Tamaki rig. After the objective measurements we made recordings of the near-field sound radiated from both the concrete slab floor and all the LTF floors for use in the subjective tests. The subjective tests were carried out in a purpose built Standard Listening Room conforming to the IEC standard IEC 268-13. 6.3
PREVIOUS RESEARCH ON SUBJECTIVE ACCEPTABILITY
Concern over impact sound insulation is obviously not confined to Australia and New Zealand and important features of the prevailing view at the time of the start of the project are illustrated in the following publications. First, a paper from Finland by Jouni Koiso-Kantilla on the topic Modern Timber Construction in Finland (see Koisi-Kantilla) includes discussion on the required sound insulation between apartments. He draws attention to the fact that the current Finnish code requirements (airborne Page 160
insulation DnTw ≥ 55; impact sound insulation Ln’w ≤ 53) are inadequate in that they do not ensure sufficient control of the low and very low frequencies. Kantilla is an advocate of a concrete topping to LTF floors citing not only improved sound insulation but benefits to fire protection (from above) and floor rigidity and he shows details of a design which achieves R’w = 60 dB and Ln’w = 49 dB with carpet and Ln’w = 52 dB with parquet. Even with this favoured floor system he comments that “surveys of residents of multi-storey timber apartment buildings indicate that, although the overall sound insulationj is excellent, special attention needs to be paid to insulating low-frequency sounds”, and the weakest points of timber inter-tenancy floors are “vibration and insulation of sounds with a frequency < 100 Hz. Current sound insulation requirements do not address either phenomenon. Based on survey results, adding a concrete pour to the top surface significantly increases its sound insulation. Therefore it is worth using concrete in inter-tenancy floors – either as part of a composite structure or as a floating floor, and other ways of increasing the mass of the floor should also be studied.” Second is a paper by Jeon and Jeon from Korea presented at the NZ Acoustical Society Conference (Nov 2004) which describes a very large study of different impact sources for exciting floors. They compared the sources for their ability to simulate the spectrum of the most-complained-about impact sounds which are (at least for Korea) those produced by children running and jumping. Their results show that for subjective testing the Impact Ball is more realistic than the sound from the tapping machine. This finding supports the inclusion of the Ball drop sounds in our test protocol. Jeon and Jeon also note that both in Korea and Japan the “impact noise standards” (equivalent to our Building Codes) require two criteria to be met (i) in the range 125- 2kHz when excited by the tapping machine, and (ii) 63- 500 Hz when excited by the Bang machine (tyre drop test). Finally from this paper, it is of value to note that their research indicates that floors which “begin to annoy/bother” people underneath are those which the tapping machine excites to Ln’Aw > 56 dB and the impact ball to Ln,FmaxAw > 54 dB. A paper by Dodd, also presented at the NZ Acoustical Society Conference 2004, discusses why a simple detectability criterion might be a preferable requirement for high quality living conditions rather than an LnTw of a certain value. Dodd argued that surveys studying loudness, noisiness, annoyance or disturbance to obtain a dose-response relationship are potentially ignoring the important issue of privacy. He suggests that we need to study privacy, and especially how it can be violated by sound, because a dwelling – i.e. someone’s home – is uniquely different from other environments in that it is where the sense of (and need for) privacy is at a maximum. He contends that privacy is likely to be more of an ‘all or nothing’ or ‘black and white’ issue and therefore any degree of your neighbour intruding into your private space by his or her sound/noise would be a violation of that privacy. Clearly the emotion aroused by this intrusion – and thus the degree of tolerance extended to it – would be influenced by the relationship experienced with the neighbour. Both laboratory experiments and the type of “survey” field experiment carried out by Jeon and Jeon fail to replicate the privacy dimension and the personal/intimate connection with a known noise producer. It is difficult to imagine how we could construct a controlled experiment in which these issues would be included and monitored. However, it is obvious that the problem of privacy invasion would be completely solved if no noise were heard and hence nonaudibility of impact sounds from normal activities is clearly what buildings should provide.
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6.4
IEC LISTENING ROOM
Our decision to carry out the subjective tests in a special listening room was a conscious departure from usual laboratory listening experiments which are typically undertaken either in an anechoic room or in a normal room using headphone presentation. Our purpose in building and equipping the listening room for this work was threefold (a) to have test conditions as near to real domestic conditions as possible – both visually and acoustically (b) to avoid artificialities that are introduced by free field (i.e. anechoic chamber) or headphone listening (c) to have continuity with the most recent and relevant overseas work carried out at the Danish Technical University (see Mortensen) The International Electro-technical Committee (IEC) requirements for listening rooms are intended to provide acoustical conditions near to domestic conditions - for the purposes of comparative listening tests on loudspeakers. In satisfying these requirements our room avoids undue effects from pronounced room resonances and long reverberation times. In addition we furnished it to represent a domestic environment. This was in order to respect the fact that there is an interaction – as yet largely un-researched - between the visual and acoustical aspects of spaces.
Figure 6–1. View of the ARC Listening Room conforming to IEC 268-13 Page 162
Our original intention was to ask subjects to compare the concrete and LTF designs for (i)
Loudness,
(ii)
Annoyance,
(iii)
Noisiness, and
(iv)
Disturbance
when listening to the constructions excited by a full range of standard and domestic impact sources (i)
the ISO standard tapping machine,
(ii)
the Japanese standard impact ball,
(iii)
tyre drop (i.e. equivalent to Japanese heavy impact or “Bang” machine),
(iv)
a male walker, and
(v)
dropped cutlery
but time constraints precluded this. Therefore, in a shortened test protocol we asked subjects to compare the reference concrete structure with selected LTF floors when excited by (1) the standard tapping machine, (2) the standard Japanese ball drop, and (3) a male walker (72 kg in weight and wearing outdoor shoes with modern composition soles). In a later stage of subjective testing (to begin in 2006) we plan to use the impact sound recordings in a fuller Multi-Dimensional Scaling (Factor Analysis) experiment to identify the subjective dimensions which control annoyance, preference etc. We then hope to relate these subjective dimensions to components in the sounds and identify physical features of the floors which control them. 6.5
OBJECTIVE EVALUATION OF PERFORMANCE
Normalized impact sound pressure levels are typically measured in 1/3rd octave bands. This means that each construction is described by 27 individual SPL values. In order to make ranking of the floors straightforward in terms of their subjective acceptability we ideally need to combine these 27 values into a single-figure evaluation. This processing into a single figure should be done in manner which guarantees the same level of acceptability against impact sound– whatever the construction type! However, when we are dealing with sound we are actually dealing with a multi-dimensional phenomenon where detail in different parts of the spectrum can lead to independent subjective effects and, consequently, we may require a more complex processing than the simple ‘weighting curve’ approach that is used in IIC and Ln’w. We readily distinguish low, mid and high frequency content in the sounds we hear. Floors of different construction can be expected to radiate differing amounts of low, mid and high frequency sound and the subjective reaction to a particular floor’s performance will depend on the particular mix of strengths of these several components produced by a specific source. The idea that a simple spectrum shaping (as used in Ln’w and IIC) will produce a rating which is adequate over the range of mixes we can expect from differing impact sources, may not be Page 163
valid. Thus we may need separate ratings for different parts of the spectrum (see the above discussion of the paper by Jeon and Jeon) and even different acceptability criteria for differing sources! Ln’w and IIC are ratings based on the medium and high frequency regions (i.e. > 100 Hz) and worked reasonably well for conditions prevailing in the mid 20th Century. However, today’s society is fundamentally different in that it has embraced amplified sound and high-powered, wide-band audio equipment is ubiquitous in public venues (cinemas, halls, pubs), homes and even cars. A not-surprising consequence of this has been less awareness of - and constraint on personal noise-producing behaviour and, as a result, higher levels of sound and noise in the home. The effects for neighbours are compounded if homes are built using lightweight, double leaf constructions which, generally, have weak low frequency insulation. So for today’s society it is quite inadequate to rate performance only on frequencies above 100 Hz. The work of the Acoustics Laboratory of the Danish Technical University (DTH) (see Mortenson) demonstrates the importance of the low frequencies but even in that work the researchers only effectively considered frequencies down to the 50 Hz third octave band. Other work by Blazier and Dupree in the US (See Blazier and Dupree) has pointed to sound at the fundamental resonance of light floors (in some cases at frequencies as low as 10-15 Hz) as being a potentially crucial determinant of their acceptability. Clearly we need, therefore, to measure and include frequencies well below what are included in standard ratings (and even well below the extended frequency range currently being considered by ISO -see ISO 717). Hence for this project both our objective measures and the recordings for the subjective experiments have included frequencies as low as possible – the normalized impact sound pressure levels were measured down to the 12.5 Hz 1/3rd octave band and the reproduction system in the listening room had a 12 Hz lower limit for its design brief. This extension of the low frequency range would normally be considered to go beyond the normal audio frequency range. However, for some of the impact sources (e.g. the ball and tyre drops) the low frequency energy is so high that they are likely to be felt as much as heard. This consideration was important in our decision to reject the idea of using headphone reproduction for the listening tests. The recordings of the sounds were made from 4 microphones spaced across a diagonal underneath the sample floors. A “4.1” system with loudspeakers sited in the ceiling of the Listening Room was used to give directional realism to the reproduced sounds. 6.6
EXPERIMENTAL SETUP
Our aim was to let listeners compare and contrast the sounds through different floor structures as if they were living underneath the floor/ceiling structures. We wanted listeners to be able to switch between the pairs of presented sounds in a so-called Paired Comparison Test or Two Alternative Forced Choice test (see ASTM E 2263-04) as often as they would like. The most advanced method for making recordings for subjective assessments uses a dummy head (See Johansson). But we decided against making dummy head recordings because i) they contain the ‘acoustics’ of the environment in which the recordings have been made. In the case of our floor test rig this would contrast markedly with the much lower reverberation expected in a dwelling ii) they involve potentially confounding effects caused by differences between the geometry of the dummy head and that of the subject8
8
This results in subtle but important differences in the so-called Head Related Transfer Functions. Page 164
Instead we made recordings in the ‘near field’ of the test ceilings (at 75 mm from the ceiling surface) in order to record mainly the direct sound radiated and thus minimise the contribution of the acoustics of the rig. This approach was validated by a check that the re-recorded sound fields at the listener position in the listening room matched the predictions of the Ln values (normalised impact sound levels) when adjustment for the different room RT was made. The criterion for this was that the values should be within +/- 2 dB (i.e. within one difference limen for an average listener). This was reached over a majority (i.e. 80 Hz – 1.25 kHz) of the relevant audio range but at lower frequencies there were larger discrepancies. In the original setting up of the listening room we did not give sufficient thought to how high the very low frequency sound levels would need to be to recreate the recorded levels. We aimed to at least match the response achieved in the Danish IEC Listening Room (but extended down to 10 Hz if possible) which had a 1/3 octave band flat response within +/- 5 dB. This we achieved down to 16 Hz for band levels of 85 dB (see Figure 3), but some of the poorer performing floors under heavy impacts (e.g. tyre drop) the power was inadequate and the loudspeakers overloaded. A special sub-woofer to handle higher infrasonic levels has recently been added to the system and will be used in a second stage of subjective assessments. We decided that the listening environment in addition to meeting the IEC criteria for a standard listening room (see figure 4 for the RT of the room) should give the feeling of being – as far as possible – a domestic environment. Therefore it was furnished appropriately.
Figure 6–2. The frequency response of the 4.1 reproduction system in the Listening Room measured at the listener’s position.
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Figure 6–3. The Reverberation Times of the Listening Room
6.7
THE SUBJECTS AND THEIR TASK
31 subjects took part (20 males and 11 females) chosen to give a wide age range (mean age 31 years; the youngest being and the oldest 61). They were not selected or screened for their experience of living in flats or apartments, nor were they screened for normal hearing – although they were asked to indicate if they were aware of any hearing deficiencies or problems. The number of subjects was based on what was sufficient for the purposes of the test but also reasonable from the point of view of the resources and time available. Considering the need to be able to distinguish preferences for one floor system over another with reasonable certainty the minimum number required to do this was 309. 9 floor systems were used in the test (the concrete reference floor (Floor 0), and sample Floors 2, 3, 8, 9, 14, 18, 19, & 20 ). The impact sounds used were (1) the tapping machine, (2) the standard ball drop, and (3) a male walker. For the latter, recordings were made with the constructions both bare and in some cases covered with carpet plus underlay. However, since the recordings of walking on carpet and underlay were incomplete the results are omitted from this experiment. The recordings were paired so that a “test” comprised the subject listening to the pair in sequence and answering set questions. One of the pair of sounds presented was always that from the reference floor but the impact source was the same for each of the pair. The 9 possible floor pairs and 4 different types of excitation gave 32 tests in all. Subjects sat in front of a computer screen displaying the test number and two icons marked A and B. By a mouse ‘click’ on the appropriate icon the listener could play the associated sounds and switch between the sounds as often as they desired. They were then asked to make a choice of which floor they would prefer to live under (see Section 6.11 for the questions and the Privacy and Noise Sensitivity questionnaires). The procedure was thus the so-called ‘2 Alternative Forced Choice’ (2AFC) procedure with no ties allowed10. 9
The sensitivity of the test is, in part, a function of two competing tasks – the risk of declaring a preference when there is none (i.e. α-risk) and the risk of not declaring that a preference exists when there is a preference (i.e. βrisk). 30 subjects gives the test a power to conclude that at least 70% of the population prefer a particular floor with α-risk = 20% and β-risk = 10%. (See ASTM E 2263-04 for more details). 10 With hindsight it is clear that ties should have been allowed and this is planned for the next stage of testing. Page 166
In a further question the subjects were asked to indicate by marking on a continuous scale how different the sounds were. The intention was to use the size of these differences from the standard/reference concrete floor to provide a ranking of the different floor constructions relative to one another. However, it became evident that subjects have approached this difference judgement in two ways i) on the basis of the strength of their preference, and ii) on the basis of the strength of perceptible differences in the timbre and character of the sounds and from interviews with a small number of the subjects it appears these approaches may not correlate. However, the results from the 2AFC question do in general support the rankings found by the above method. For example equality of preference for a particular timber construction and the concrete reference floor would be expected to result in a 50/50 preference score and as the performances diverge we expect this to be reflected in greater differences in the preference scores. Hence the relative size of the scores in each pair can be used to rank order the floors. Additional questions invited listeners to describe what qualities in the sounds they perceived as different. Very few subjects made use of this option and therefore these questions were essentially redundant. 6.8
RESULTS AND DISCUSSION
Table 1 shows the ranking of the floors derived both from the preference scores11 and the subjective difference judgements. Apart from some minor inversions in the orders it clear that the two techniques are in agreement. Major differences in the rankings are evident, however, as the impact source changes. The results presented are the mean judgements of the subjects12. Tapping machine
Ball drop
6.9
WALKING ON BARE FLOOR
Ranking by preference
Ranking by Subjective difference
Ranking by preference
Ranking by Subjective difference
Ranking by preference
Ranking by Subjective difference
fl 9 fl 8 fl 18 fl 3 fl 19 fl 14 fl 20 fl 2 Ref fl
fl 9 fl 8 fl 18 fl 3 fl 14 fl 19 fl 2 fl 20 Ref fl
Ref fl fl 9 fl 8 fl 19 fl 18 fl 14 fl 20 fl 3 fl 2
Ref fl fl 9 fl 8 fl 19 fl 20 fl 3 fl 14 fl 18 fl 2
fl 9 1 fl 3 2 Ref fl 3 fl 18 4 fl 8 5 fl 14 6 fl 20 7= fl 19 7= fl 2 7=
fl 9 fl 3 Ref fl fl 8 fl 18 fl 14 fl 20 fl 19 fl 2
1= 1= 1= 1= 1= 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7= 7= 7=
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
Table 6–1: Ranking of floors by Preference score and by Subjective Difference
11
The markings on the continuous scale were translated into numerical values between 0 and 10 by taking the length of the scale as 10 and measuring to an accuracy of 0.1.. 12 These are not always for the total 31 subjects as occasionally subjects gave no answer for either the A/B preference or alternatively for a subjective difference. Presumably these were occasions when they felt that the two floors tied. However, totals always equalled or exceeded 25. Page 167
The cohort of subjects was too small to allow any clear indications of differences between subjects of significantly different Noise Sensitivity or Privacy Rating. When the subjects were divided into Low, Average and High groups for Noise Sensitivity and Privacy Rating the results showed no consistent trend, - but with such small numbers of subjects in the extreme groups (e.g. the High Noise Sensitivity and Low Privacy Rating groups each comprised only 3 subjects) this cannot be relied on as indicating no dependency. When divided by sex a small but consistent difference between men and women was evident (e.g. an average of 0.3213 for the tapping machine and 0.5314 for the Ball drop) with women judging differences overall to be slightly smaller. When the subjects were divided into two age groups first those aged 40 (n=10) the judgements were not different for the tapping machine sounds but for the Ball drops the younger subjects consistently judged the differences larger by an average of 1.215. Apart from providing a direct indication of the relative satisfaction to occupants of LTF and standard concrete floor constructions we hoped that the subjective experiment results would help clarify if existing objective measures are adequate for ranking occupant preference. The issue here is that the standard building insulation measures – even with the ISO low frequency extensions – don’t cover the full bandwidth used in this experiment. However, Loudness (in Sones) and A-weighted SPL are both standardised measures and can be extended to include all the low frequencies (see Appendix 3 for the Loudness calculation) and the correlations between these and the subjective preference scores are shown in figures 5 to 7. The results show surprisingly good correlations for both the A-weighted SPL (Leq 10s) and Loudness with the subjective judgements. The plots and the R2 values are obtained from the mean values of the subjects in each case16. It is well understood17 that we cannot use individual results to obtain trends and relationships because of the range of factors (like Noise Sensitivity and Privacy Rating) which come into play.
13
These values are distances on the continuous scale of total length 10. As note 3. 15 See footnote 3 on previous page. 16 Where values are –ve this indicates that the floors are less preferred than the concrete reference floor 17 For example van Dongen states that measures “used at individual (personal) level can not predict or have little predictive value of the noise annoyance experienced from neighbouring dwellings”. 14
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Average Loudness against Subjective Difference 14 12 10
Loudness (Sones)
8 Linear (Loudness (Sones))
6 4 2 0
y = -1.1631x + 13.093 0
2
4
6
8
10
2
R = 0.8364
Subjective Difference
Figure 6–5(a) Relationship between the Subjective Differences and Loudness (Sones) when the floors excited by the tapping machine.
Leq(A) against Subjective Difference 70 60 50
Leq(A) Linear (Leq(A))
40 30 20 10 0 0
2
4
6
8
10
y = -2.1457x + 60.883 2 R = 0.6501
Subjective Difference
Figure 6–5(b) Relationship between the Subjective Differences and A-weighted SPL (Leq 10s) when the floors are excited by the tapping machine.
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Average Loudness against Subjective Difference 3.5 3 2.5
Loudness (Sones)
2 Linear (Loudness (Sones))
1.5 1 0.5 0 -8
-6
-4
-2
y = -0.3748x + 0.6011 2 R = 0.8525
0
Subjective Difference
Figure 6–6(a) Relationship between the Subjective Differences and Loudness (Sones) when the floors excited by the ball drop.
Leq(A) against Subjective Difference 50 40 Leq(A) Linear (Leq(A))
30 20
y = -2.3394x + 29.173 2
R = 0.8299
10 0 -8
-6
-4
-2
0
Subjective Difference
Figure 6–6(b) Relationship between the Subjective Differences and A-weighted SPL (Leq 10s) when the floors are excited by the ball drop.
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Average Loudness against Subjective Difference 0.6 0.5 0.4
Loudness (Sones)
0.3
Linear (Loudness (Sones))
0.2 0.1
y = -0.0359x + 0.3323 2 R = 0.5416
0 -6
-4
-2
0
2
4
Subjective Difference
Figure 6–7(a) Relationship between the Subjective Differences and Loudness (Sones) when the floors excited by walking on the bare floor.
Leq(A) against Subjective Difference 30 25 Leq(A) Linear (Leq(A))
20 15 10 5 0 -6
-4
-2
0
2
4
y = -0.547x + 22.442 2 R = 0.5001
Subjective Difference
Figure 6–7(b) Relationship between the Subjective Differences and A-weighted SPL (Leq 10s) when the floors are excited by walking on the bare floor. The rankings consistently show floor 9 as either close to, or better than, the concrete reference construction whatever the impact source or floor covering. But can we conclude that overall it is as satisfactory a construction as the concrete slab? The critical condition is when the floor is subjected to heavy impact where the Loudness and A-weighted SPL results and the subjective preferences do distinguish the floors as different (we can note that Ln’w and IIC values are not helpful here because the tapping machine has such a different excitation spectrum!). However, are these differences likely to be significant and to make the floors differ in the acoustic comfort they provide?
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Guidance can be found from the way in which “semantic difference scale” processing has been carried out in other research on subjective judgements. We processed our scale with a resolution of 1 % but others divide their scales into categories with a much coarser resolution. For example in the most recent work (see Johansson and Guski) it is recommended to use a scale divided into only 5 categories. This would imply that subjective differences less than 2 in our results put the sounds in the same category of acoustic perception and the associated floors into the same class of acoustic comfort. This is clearly the case for floor 9 in the case of the ball drop where, although the mean preferences indicates a bias for the concrete slab floor, the subjective difference is less than 2 (i.e. 1.61 for the Ball drop). Further guidance is found in the acoustic quality categories and classes of acoustical comfort that are used in Europe (e.g. in the Nordic countries and Germany). Typically different categories or classes span a range of 5 - 7dB (see, for example, Norwegian Standard NS 8175 and German Standard VDI 4100) and so impact levels that differ by less than 5 dB would be regarded as being subjectively in the same category18. The A-weighted SPL (Leq 10s) values for floor 9 and the reference floor in the above situation, in fact differ by less than 1 dB. It therefore seems a valid conclusion from this experiment that floor 9 – and any similarly performing LTF floor structure – provides a subjectively perceived performance which is at least as acceptable as that of the 150 mm concrete reference floor19. 6.10 REFERENCES ASTM Standard E989 “Standard Classification for Determination of IIC” ASTM Standard E 2263-04 “Standard Test Method for Paired Preference Test” ISO 140-6 “Laboratory Measurement of Impact Sound Insulation” ISO 717-2 “Rating of Sound Insulation in Buildings – Impact Sound Insulation” JIS A 1418 “Measurement of Floor Impact Sound Insulation of Buildings – Heavy Impact Source” Japanese Industrial Standard NS 8175 “Sound Conditions in Buildings” Norwegian Standard VDI 4100 “Noise Control in Housing” German standard Blazier W.E. & Dupree R. (1994) “Investigation of low-frequency footfall noise in woodframe, multifamily building construction” JASA 96(3), pp. 1521-1532 Grimwood, C. (1995). “Complaints about poor sound insulation between dwelling”, IOA Acoustics Bulletin 20, pp11-16. Guski, R. (1997). “Psychological methods for evaluating sound quality and assessing acoustic information”, Acta Acustica 83, 765-774 Johansson, A-C. (2005). “Drum sound from floor coverings – Objective and Subjective Assessment”, PhD Thesis, Lund University (ISBN:91-628-6531-5) Koisi-Kantilla, J. (2005). “Modern Timber Construction in Finland”, Dept of Architecture, University of Oulu
18
This is consistent with the 5 dB increments that are used in audiometry in order to create level changes which are just noticeable to the average listener. 19 At least for the range of “normal” impacts represented by the sources used in this experiment, but, as the reproduction system did not adequately reproduce the very lowest frequencies, confirmation is necessary from the next stage of planned subjective testing. Page 172
Mortensen, F. R. (2000). “Subjective Evaluation of Noise from Neighbours – with Focus on Low Frequencies”, Publication 53, Dept of Acoustic Technology, Technical University of Denmark van Dongen, J. E. F. (2001). “Noise Annoyance from Neighbours and the impact of sound insulation and other factors”, Inter-Noise 2001, The Hague, Netherlands.
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6.11 QUESTIONNAIRES USED IN THE SUBJECTIVE TESTING 1. Listener Instruction Sheet You will be presented a sequence of sound pairs. For each pair of sounds we would like you to make judgements according to the questions below. For each presented pair you may listen to the two sounds as many times as you like in order to make your judgement – simply click the boxes on the screen marked A or B TEST 1 1) Imagine you are in a flat or apartment (which you own) and you hear sounds from an above flat/apartment on a regular basis. If the two sounds A and B are options resulting from different possible building constructions/types which would you prefer to have to live with? A
or
B
(Please tick one) 2) How different do you judge the 2 sounds A and B to be? Please indicate your judgement by placing an X on the following scale:
———————————————————— Not significantly different
Noticeably different
Markedly different
(Note: This is a continuous scale so place your mark to indicate your precise judgement)
3) Describe any difference(s) that you can hear between A and B in (a) loudness:
(b) sound quality:
(c) any other features (please elucidate): -------------------------------------------------------------------------------------------------------
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2. Privacy Questionnaire
1) What does Privacy mean to you?
2) We sometimes use the term "Private dwelling". What do you feel is being conveyed that is different from if we had simply used the term "dwelling"?
3) Please give examples of actual or imagined events where you would consider your privacy as having been violated/invaded. (Please provide as many as you feel able but at least 2 examples.)
4) With respect to the place where you currently live how would you rate its privacy: Grossly lacking
Completely private
5) If you have not marked 'Completely private' above please indicate (a) those features/issues which are the reasons for its incompleteness
(b) what changes - in order of importance - would be needed to make your dwelling completely private
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6) How important is privacy for you? Of no significance
Essential
Please give reasons for your answer:
7) Considering, now, the wider community: (a) What contribution does privacy make, in your view, to its welfare?
(b) Are present provisions sufficient to optimise that contribution? If not, what changes/additions are needed?
(c) What efforts, if any, are you conscious of making to promote privacy for others?
Please describe briefly the type of dwelling you live in (e.g. detached house, apartment, townhouse) and its construction details (e.g. weatherboard, single storey brick and tile, apartment block in concrete)
9) Your personal profile. (a) Name (optional): Home
(town/city/RD):
Age: Sex: Occupation: Importance/relevance of music to your life: can take it or
of some
significant Page 176
of major value
essential
leave it
interest
(b) Do you live with others (e.g. part of a family or a shared flat)? If yes, (i) please describe who and how many:
YES/NO
(ii) describe whether you feel they are noisy or not and whether you feel they are sensitive to others:
(c) If you have any views or observations about privacy that you feel have not been adequately covered in this questionnaire please write them here:
3. NOISE SENSITIVITY QUESTIONNAIRE Please circle the number corresponding to your attitude to the following statements 1. I wouldn’t mind living in a noisy street if the apartment/house I had was nice 1 Agree strongly
2
3
4
5 Disagree strongly
6
4
5 Disagree strongly
6
2. I am more aware of noise than I used to be 1 Agree strongly
2
3
3. No one should mind much if someone turns up the their stereo full blast once in a while 1 Agree strongly
2
3
4
5 Disagree strongly
6
4. At the cinema (or theatre or concerts), other people whispering and crinkling sweet wrappers disturb me 1 Agree strongly
2
3
4
5 Disagree strongly
6
3
4
5 Disagree strongly
6
5. I am easily awakened by noise 1 Agree strongly
2
6. If it is noisy where I am studying, I try to close the door or window or move to somewhere else
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1 Agree strongly
2
3
4
5 Disagree strongly
6
4
5 Disagree strongly
6
7. I get annoyed when my neighbours are noisy 1 Agree strongly
2
3
8. I get used to most noises without much difficulty 1 Agree strongly
2
3
4
5 Disagree strongly
6
9. How much would it matter to you if an apartment/house you were interested in renting was located across the street from a fire station 1 Very much
2
3
4
5
6 Very little
10. Sometimes noises get on my nerves and make me irritated 1 Agree strongly
2
3
4
5 Disagree strongly
6
11. Even music I normally like will bother me if I’m trying to concentrate 1 Agree strongly
2
3
4
5 Disagree strongly
6
12. It wouldn’t bother me to hear the sounds of everyday living from neighbours (footsteps, running water, etc) 1 Agree strongly
2
3
4
5 Disagree strongly
6
13. When I want to be alone, it disturbs me to hear outside noises 1 Agree strongly
2
3
4
5 Disagree strongly
6
14. I’m good at concentrating no matter what is going on around me 1 Agree strongly
2
3
4
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5 Disagree strongly
6
15. In a library, I don’t mind if people carry on a conversation if they do it quietly 1 Agree strongly
2
3
4
5 Disagree strongly
6
16. There are often times when I want complete silence 1 Agree strongly
2
3
4
5 Disagree strongly
6
17. Motorcycles ought to be required to have better/bigger mufflers 1 Agree strongly
2
3
4
5 Disagree strongly
6
4
5 Disagree strongly
6
18. I find it hard to relax in a place that is noisy 1 Agree strongly
2
3
19. I get angry with people who make a noise that keeps me from falling asleep or getting work done 1 Agree strongly
2
3
4
5 Disagree strongly
6
20. I don’t mind living in an apartment with thin walls 1 Agree strongly
2
3
4
5 Disagree strongly
6
3
4
5 Disagree strongly
6
21. I am sensitive to noise. 1 Agree strongly
2
22. I get irritated if I hear a child screaming in a public place. 1 Agree strongly
2
3
4
5 Disagree strongly
6
23. I tolerate people who talk behind me during meetings, lectures or concerts 1 Agree strongly
2
3
4
5 Disagree strongly
6
24. When I choose a restaurant I am not concerned whether there will be loud music. Page 179
1 Agree strongly
2
3
4
5 Disagree strongly
6
25. In a car I accept the noise of people slamming the doors. 1 Agree strongly
2
3
4
5 Disagree strongly
6
26. I have no reaction to hearing music or its beat from passing cars. 1 Agree strongly
2
3
4
5 Disagree strongly
6
27. I am annoyed when I turn on the TV if the volume has been left too loud 1 Agree strongly
2
3
4
5 Disagree strongly
6
4
5 Disagree strongly
6
4
5 Disagree strongly
6
28. I am often conscious of how loud I am speaking 1 Agree strongly
2
3
29. I like to have music playing while I work 1 Agree strongly
2
3
30. More emphasis should be given to headphones as an alternative to loudspeakers 1 Agree strongly
2
3
4
5 Disagree strongly
6
31. My family (or others I live with) make noises which irritate me. 1 Agree strongly
2
3
4
5 Disagree strongly
6
32. Not creating noise was an issue during my upbringing 1 Agree strongly
2
3
4
5 Disagree strongly
6
33. When I have a guest for a meal I will put on background music 1 Agree strongly
2
3
4
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5 Disagree strongly
6
34. When I eat or relax outdoors in summer I like to have music playing. 1 Agree strongly
2
3
4
5 Disagree strongly
6
35. If my car develops a rattle (but clearly not an engine or mechanical problem) I can easily ignore it 1 Agree strongly
2
3
4
5 Disagree strongly
6
36. When driving I am attentive to the sound of the car engine 1 Agree strongly
2
3
4
5 Disagree strongly
6
37. There are some types of clothes I don’t wear or don’t like wearing because the material/fabric makes a noise 1 Agree strongly
2
3
4
5 Disagree strongly
6
38. I am conscious of the sound of knives and forks on plates at meal times 1 Agree strongly
2
3
4
5 Disagree strongly
6
39. At home I don’t mind the noise of the vacuum cleaner, hairdryer, food mixer etc 1 Agree strongly
2
3
4
5 Disagree strongly
6
40. I am not embarrassed by personal sounds when I use the toilet 1 Agree strongly
2
3
4
5 Disagree strongly
6
41. I choose destinations for my holidays where I can be assured of peace and quiet 1 Agree strongly
2
3
4
5 Disagree strongly
6
42. I find myself involuntarily tracking the movements of others by the sounds they make 1 Agree strongly
2
3
4
Do you think your hearing is normal? Page 181
5 Disagree strongly
6
Yes
No
If no, please briefly describe your hearing difficulty:
Please indicate if there are any questions included in the above which surprise you (and say why), and also please suggest questions which could be valuable to include because you feel they would be especially revealing.
Surname (optional):
First name:
Country of origin: Nationality: Sex: M
Profession: F
Age:
THANK YOU VERY MUCH FOR YOUR ASSISTANCE
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Date:
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