Evaluation of Structural Sound Path Modification Methods for the

AIA-DAGA 2013 Merano

Evaluation of Structural Sound Path Modification Methods for the Reduction of Structure-Borne Sound Transmission in Aircraft Fuselage Structures Felix Langfeldt1∗ , Fabian T. Seebo1 , Wolfgang Gleine1 , Otto von Estorff2 1

1

Hamburg University of Applied Sciences, 20099 Hamburg, Germany 2 Hamburg University of Technology, 21073 Hamburg, Germany ∗ E-mail: [email protected]

Introduction

With the worldwide increasing demand for an environmentally friendly aircraft, the counter-rotating open rotor engine technology seems to be a promising alternative for powering future aircraft generations. However, the acoustical properties of these engines with fundamental blade passing frequencies in the low-frequency regime (around 100 Hz) and peak sound pressure levels of over 150 dB [8, 9] are challenging. While state-of-the-art aircraft fuselage design is primarily motivated by aspects of structural strength, the vibro-acoustical properties of a fuselage structure could be significantly improved – especially in this difficult frequency regime – by considering both mechanical and acoustic design aspects. In this paper, a modification of the interconnection between two fuselage sections is proposed as a new structural design approach to attenuate structure-borne sound waves travelling from one section to the other. Three models of different complexity have been created and investigated to evaluate the influence of the modifcation.

2

Description of the Modification

Typically, two aircraft fuselage sections are interconnected by circumferential skin doublers and stringer splice fasteners, which result in a quasi-continuous transmission of loads along the interconnection [7]. However, this traditional interconnection design is expected to yield only little resistance to incoming structural sound waves. Therefore, it seems reasonable to increase the dynamic decoupling between two fuselage sections by introducing modifications to the traditional design, which effectively attenuate the propagation of low-frequency structure-borne sound between two fuselage sections. The structural sound path modification proposed in this paper involves the following passive mechanisms: (I) (II) (III) (IV)

Discontinuation of the fuselage skin and stringers, discontinuation of mass distribution, multiple redirection of structural waves and pointwise structure-borne sound bridges.

The structural realization of these mechanisms by modifying the traditional interconnection design is illustrated in Figure 1. The first mechanism is realized by physically disconnecting the skins and stringers with a gap. Thus, it is expected that the dynamic decoupling performance

frames

(II)

bolts (IV) (I) (III) Figure 1: Illustration of the proposed modified interconnection design.

of the interconnection can be improved compared to the quasi-continuous traditional design. A further improvement is anticipated through the blocking-mass effect caused by the additional frame and bolt masses, leading to a non-continuous mass distribution (mechanism II). Thirdly, the structure-borne sound waves are forced to pass through multiple redirections along the frames and the bolts, which are located with a radial offset from the skin plane. The bolts also serve as a point-wise sound bridge, thus realizing the last of the four structure-borne sound attenuation mechanisms.

3

Modelling

To evaluate the dynamic decoupling performance of the modified interconnection, three different models have been created: A full-scale fuselage model for numerical analyses, a simplified plate model for experimental and numerical studies and a beam model for basic physical studies. In the following sections, these models are briefly presented. For more detailed descriptions of the modeling process, the reader is referred to [6].

3.1

Fuselage Model

An overview of the simplified fuselage model, including stringers and interconnections, is given in Figure 2. As a first approach to study the interconnection properties, frames are neglected in the model. The fuselage geometry is based upon [5, 10], where an A320-like fuselage structure has been investigated. A comprehensive list of all chosen dimensions is given in Table 1. The material of all fuselage components except for the bolts was chosen to be aluminium, with density ρAl = 2700 kg/m3 , Young’s modulus EAl = 72 GPa and Poisson’s ratio µAl = 0.34. The bolt’s material, on the other hand, was steel (ρSt = 7800 kg/m3 , ESt = 210 GPa and µSt = 0.31). For the finite element analysis of the fuselage model, the fuselage skin was discretized with 120x620 (axial x

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AIA-DAGA 2013 Merano Table 1: List of the fuselage model dimensions.

Fuselage L = 10 m R=2m t = 1.5 mm

Stringer bS = 40 mm hS = 40 mm tS = 2 mm NS = 72

bS

stringer:

L

hS

Fˆz

Doubler bD = 80 mm tD = 3 mm

t

tS

doubler: θF r θ

x

xF sec

R

#1

n

tio

s

ion ect

#2

frames and bolts:

bD

tD

bF lB

hB

hF tF

∆hB

Figure 2: Geometry of the simplified fuselage model, stringers and interconnection elements.

circumferential direction) CQUAD4 shell elements per section. The stringers, doubler and frames were also modeled using shell elements and rigidly connected to the fuselage, while the bolts were discretized with CBAR beam elements. The boundaries of the fuselage model were unconstrained (free-free boundary conditions) and fluid-structure coupling was not considered, i.e. the structure was analyzed in vacuo.

3.2

Plate Model

For experimental studies and comparison with further simulations, a simplified flat plate model was derived from the fuselage geometry presented above. An isometric view of the plate model geometry is given in Figure 3. The model is composed of two plates longitudinally

a ˆ+ z,i Fˆz

B0

Frame bF = 40 mm hF = 120 mm tF = 3 mm

Bolt lB = 20 mm hB = hF /3 ∆hB = hB DB = 10 mm

dynamic response of both model halves to a driving point force has been measured using six accelerometers per plate. The force excitation spot and the accelerometer locations are indicated in Figure 3. The numerical setup of the plate model is similar to the fuselage model and the dynamic excitation and acceleration processing has been carried out at the same locations as in the experiment. To approximate the string-suspension conditions in the experiment, all boundaries of the plate model were selected to be free.

3.3

Beam Model

For the analysis of the basic physical principles and sensitivities to changes in e.g. the geometry or boundary conditions, a beam model was derived from the plate model by condensing the two-dimensional plate properties to one-dimensional Euler-Bernoulli beam members. The investigations were performed numerically using the dynamic stiffness matrix approach [1].

4

Results

The attenuation of structure-borne sound caused by the section interconnection has been quantified using the transmission loss TL, which generally is given by TL = −10 log τ ,

(1)

where τ is the transmission factor. τ can be expressed as the ratio of the spatially averaged vibrational energies − of the recieving section hEi and the excited section + hEi [2]. These quantities can be estimated by the arithmetic average of the squared surface normal velocity amplitudes on the skin of each section [4]

a ˆ− z,i N m X 2 hEi ≈ |ˆ an,i | , N ω 2 i=1

0

L

Figure 3: Isometric view of the plate model including excitation spot and accelerometer locations.

stiffened by three stringers, leading to an approximate plate width of B 0 = 500 mm ≈ 3 · (2πR/NS ). Both plates have a length of L0 = 2 m, which roughly corresponds to a bending wave length at 100 Hz, and are interconnected at one edge by exchangeable interconnection designs. Owing to the modularity of the model, the traditional section interconnection design could not be realized with continuous stringers. Instead, a doubler plate of thickness tD was used to connect the two plates in this case. The stringers, however, could not be exchanged and thus remained disconnected. The measurements were performed in an anechoic chamber, where the model was vertically suspended from two elastic strings attached to the chamber ceiling. The

(2)

where m ist the section mass, ω = 2πf the angular frequency, N the number of acceleration evaluation points on the skin of each section, and a ˆn,i the surface normal acceleration amplitude on point i. Taking into account that, due to symmetry, both sections have the same mass and number of nodes, the following approximative expression for TL is obtained: PN + 2 ! ˆn,i i=1 a TL ≈ 10 log PN (3) 2 . a ˆ− i=1

n,i

To evaluate the influence of the modified interconnection design on the structure-borne sound attenuation between the sections, quantified by the calculated transmission loss TLmod , the TL of the traditional interconnection

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design TLtrad is taken as a reference. Thus, the difference ∆TL = TLmod − TLtrad corresponds to the vibroacoustical “yield” of the modified interconnection design: A positive ∆TL means an improved decoupling between both fuselage sections and vice versa. Therefore, this quantity is utilized in the current paper for the evaluation of the section interconnection design modification. The frequency range of interest for all investigations was chosen to be f = 20 to 400 Hz, since the proposed modification is meant to be effective at lower frequencies. To analyze the influence of the frame geometry in the modified section interconnection design, additionally to the reference frame height of 120 mm a smaller frame height of hF = 80 mm has been investigated.

4.1

Beam Model

To gain an insight into the basic physical principles governing the vibro-acoustic properties of the interconnection modification, the beam model was analyzed with non-reflecting boundary conditions. The results obtained for the two different frame heights are given in Figure 4. Additionally, the results of the theory of blocking masses

∆TL

80 dB 60

hF = 120 mm: model theory

hF = 80 mm: model theory

∆TL

L→∞ L=2m L = 2 m (av. ∆TL) L = 10 m L = 10 m (av. ∆TL)

20 0

−20 0

50

100

150

200 f

250

300

350 Hz 400

Figure 5: Beam model results for the model length influence.

the more local extrema are introduced due to the growing number of eigenmodes in the considered frequency range. These eigenmodes lead to a clear difference between the finite and infinite models, which make the physical interpretation of finite model results difficult. To overcome this difficulty, the finite model results are arithmetically averaged in third octave bands, which is also shown in Figure 5. Though this averaging leads to a loss of detail, for L = 10 m a good approximation of the infinite model results is obtained, especially above the peak frequency. Therefore, the averaged results are considered in the further investigations. For the sake of completeness, however, the narrow-band results are kept inside the plots.

4.2

40

Plate Model

The measurement and simulation results of the plate model with the two different frame heights are shown in Figure 6. In both cases, the averaged results of the

20 0 0

60 dB 40

50

100

150

200 f

250

300

350 Hz 400 60 dB 40 ∆TL

Figure 4: Comparison of infinite beam model results and blocking mass theory (according to [3]).

on beams [3] are shown for the different frame heights, when the properties (mass and mass moment of inertia) of the interconnections are applied to the theory. It can be seen, that the beam model ∆TL-values have a distinct peak at a specific frequency, which shifts to higher values as the frame height is decreased. Above the peak frequency, ∆TL decreases quickly to a constant value of around 10 dB. These two findings are reflected by the blocking mass theory, which suggests, that the blocking mass mechanism is one of the fundamental physical processes in the vibro-acoustical behaviour of the modified interconnection design. Real structures, however, always have finite dimensions with boundaries, that usually reflect all or some part of the incoming structure-borne sound wave energy. In the case of the experimental and numerical models investigated in this work, this leads to the developement of standing waves that are generated by superposition of partially reflected (at boundaries and interconnection joints) and transmitted structure-borne sound waves. To investigate the effect of finite model lengths, the beam model has been simulated for different lengths L = 2 and 10 m as well as L → ∞. The results are shown in Figure 5. In this figure a clear dependence of ∆TL on the model length can be seen: The longer the finite model,

Sim. Exp.

av. ∆TL av. ∆TL

20 0

−20 0

50

100

150

200 f

250

300

350 Hz 400

(a) hF = 120 mm.

∆TL

60 dB 40

Sim. Exp.

av. ∆TL av. ∆TL

20 0

−20 0

50

100

150

200 f

250

300

350 Hz 400

(b) hF = 80 mm.

Figure 6: Plate model measurement and simulation results.

experimental and numerical models agree qualitatively quite well. When comparing the averaged results of the plate model and the beam model in Figure 6a and Figure 5, respectively, it can be seen, that the averaged curves have resembling shapes with a slight local maximum in the range between 100 and 150 Hz.

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This suggests a similar influence of the blocking mass effect as in the beam model, which can be endorsed by investigating the plate model results with a lower frame height in Figure 6b, where a shift of the local maximum to a higher frequency is visible in both experimental and numerical results. At frequencies above the location of the local maximum, however, the transmission loss differences of the plate models decrease steadily and seem to tend towards zero, which was not found in the beam model investigations. From the available data no physical explanation of this behaviour could be found. It is possible, however, that the incidence of oblique bending waves, which cannot be replicated by the beam model, is a reason for this observation.

4.3

acoustic effect of the section interconnection modification. The ∆TL-dropoff at higher frequencies, however, could also be identified in this case.

Acknowledgements This work has been performed under the framework of the LuFo IV-4 project Comfortable Cabin for LowEmission Aircraft (COCLEA), funded by the Federal Ministry of Economics and Technology, which is gratefully acknowledged by the authors.

References [1] J.R. Banerjee. Dynamic Stiffness Formulation for Structural Elements: A General Approach. Computers & Structures, 63(1):101–103, 1997.

Fuselage Model

[2] C. Boisson, J.L. Guyader, P. Millot, and C. Lesueur. Energy transmission in finite coupled plates, part II: Application to an L shaped structure. Journal of Sound and Vibration, 81(1):93–105, 1982.

Finally, the simulation results of the fuselage model for hF = 120 and 80 mm are given in Figure 7. The

∆TL

60 dB 40

hF = 120 mm 80 mm

av. ∆TL av. ∆TL

[3] L. Cremer, M. Heckl, and Bj¨orn A.T. Petersson. Structure-borne Sound: Structural Vibrations and Sound Radiation at Audio Frequencies. Springer, Berlin, 2005.

20 0

−20 0

50

100

150

200 f

250

300

[4] K. De Langhe. High Frequency Vibrations: Contributions to Experimental and Computational SEA Parameter Identification Techniques. PhD thesis, University of Leuven, 1996.

350 Hz 400

Figure 7: Fuselage model simulation results.

[5] T. Kotzakolios, D.E. Vlachos, and V. Kostopoulos. Blast Response of Metal Composite Laminate Fuselage Structures Using Finite Element Modelling. Composite Structures, 93(2):665–681, 2011.

shape of the averaged curves is different to the averaged results of the models before. This indicates that the interconnection modification influence on the fuselage model cannot be extrapolated from the plate model results, but, in any case, a vibro-acoustical benefit of the modified design – predominantly at lower frequencies – is visible. Still, a decrease of frame height shifts the ∆TL-curve slightly to higher frequencies, but this effect is not as explicit as in the cases before. However, the dropoff of ∆TL at higher frequencies, which was already observed in the plate model and is possibly caused by oblique bending waves, is much more prevalent in the fuselage model results.

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[6] F. Langfeldt, F.T. Seebo, W. Gleine, and O. von Estorff. Reduction of Low-frequency Structureborne Sound Transfer Between Two Sections of a Stiffened Cylindrical Shell by Structural Transfer Path Modification. In Proc. of the 4th International Workshop on Aircraft System Technologies, Hamburg, Germany, 2013. [7] M.C.Y. Niu. Airframe Structural Design: Practical Design Information and Data on Aircraft Structures. Conmilit Press, Hong Kong, 1988.

Conclusions

In this paper, a new concept for an aircraft fuselage section interconnection for the efficient attenuation of structure-borne sound waves has been presented and investigated using three different models, namely a beam model, a plate model and a simplified fuselage model. The analyses of the beam model revealed, that the blocking mass effect is an important mechanism of the proposed modification, which led to an increase of the transmission loss by over 10 dB above the blocking frequency. Experimental and numerical investigations of the plate models showed, that the blocking mass influence can also be identified in this case with an unexpected decrease of ∆TL at higher frequencies. Finally, the simulations of the fuselage model confirmed the positive vibro-

[8] W. C. Strack, G. Knip, A. L. Weisbrich, J. Godston, and E. Bradley. Technology and Benefits of Aircraft Counter Rotation Propellers. NASA TM-82983, 1982. [9] A. Stuermer and J. Yin. Installation impact on pusher CROR engine low speed performance and noise emission characteristics. International Journal of Engineering Systems Modelling and Simulation, 4 (1-2):59–68, 2012. [10] M.J.L. van Tooren and L.A. Krakers. Multidisciplinary Design of Aircraft Fuselage Structures. In 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 2007. AIAA-2007-0767.

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