Acoustic Research at Bradford University. • Acoustic materials ... Extensive
experimental setup for measuring acoustic, vibration .... 24. Impact sound
insulation ...
Acoustic Porous Materials and Their Characterisation Kirill V. Horoshenkov School of Engineering, Design and Technology University of Bradford Bradford
[email protected]
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Where is Bradford on the map? Yorkshire dales
Bradford city
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Acoustic Research at Bradford University •
Acoustic materials (Prof. Horoshenkov, Dr. Swift (Armacell UK))
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General sound propagation (Prof. Horoshenkov, Prof. Hothersall*, Dr. Hussain)
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Environmental noise (Prof. Watts (TRL), Prof. Hothersall*, Prof. Horoshenkov)
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Vibration (Prof. Wood, Prof. Horoshenkov)
supported by ~15 PhD/MPhil students
(*) – visiting professor
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Experimental Facilities at Bradford University •
Sound propagation experiments
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Extensive experimental setup for characterisation of material pore structure
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Extensive experimental setup for measuring acoustic, vibration and structural performance of poro-elastic materials
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Facilities for poro-elastic material manufacturing 4
Topics of Research on Acoustic Materials •
Development of improved prediction models
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Experimental investigation of porous media
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Development of novel, environmental sustainable materials with improved acoustic efficiency
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Where these materials are actually used?
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Automotive insulation
Aircraft insulation
Noise from electronic cabinets
Pipeline insulation
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How these materials look like?
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Consolidated recycled foam
Granular mix
Virgin reticulated foam
Re-constituted foam grains
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What they actually do to sound?
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Effect on room response Propagation in empty enclosure with rigid walls
speaker
Propagation in enclosure with porous layer
mic 11
Effect on pipe response (20m long, 600mm concrete pipe)
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How these materials are characterised?
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Impedance tube method BS 10534-2 p2
microphone 2
Sound source
Stationary random noise
microphone 1
p1
∆
Rigid backing pi l mic 3
pr
tested sample
p2 eik∆ + e −ik∆ R H (ω ) = = p1 1 + R
H (ω ) − eik∆ 2ikl e R(ω ) = −ik∆ e − H (ω )
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Measuring frequency-dependent dynamic stiffness top accelerometer loading plate (m)
tested sample (Z, k)
impedance head
Z =
M ω sin kl T − cos kl
E=
Zω k
mT 2 + M k = l cos ( m + M ) T −1
−1
shaker
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Armafoam sound
Real
1.00E+06
1.00E+05 10
100
1000
frequency, Hz
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1
0.9
0.8
0.7
Loss factor
0.6
0.5
0.4
0.3
0.2
0.1
0 10
100
1000
Frequency (Hz)
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Measuring dynamic stiffness to BS29052 s = ω 02 m [ Pa / m ] top accelerometer with dynamic mass shaker
bottom accelerometer loading plate tested sample
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Dynamic Stiffness - BS29052
-20 lower stiffnes
-25
Relative acceleration level, [dB]
-30 -35
f0
-40 -45 Material 1 Material 2
-50
Material 3
-55 -60 10
100 frequency (Hz)
1000 19
Airborne transmission loss (0.5m x 0.5m plate)
tested plate
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Averaged Transmission Loss for 0.48m x 0.48m x 47 mm samples of rockwool 5
Transmission Loss, dB
-5
With skins on Without skins
-15
-2 5
-3 5
-4 5
-55
-6 5 10
10 0
10 0 0
Frequency, Hz
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Airborne transmission loss (99mm sample)
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Impact sound insulation
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Octave -band level
Relative acceleration level, dB. Re. 1V
100.0
90.0 Developed sample
80.0
Cumulus 70.0
Without material on w ooden base
60.0
50.0
40.0
30.0 10
100
1000
10000
frequency, Hz
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Acoustic Material Modelling of Porous Media
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What is required from an acoustic material model apart from being accurate?
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What else is required from an acoustic material model apart from being accurate?
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Response to a δ-pulse at t = 0 Comparison of some common impedance models. Semi-infinite layer 1000000 Pade approximation Keith Wilson (A-C-like)
Response to a δ-pulse
100000
Miki model Delany and Bazley model
10000
analytic models non-analytic models
R = 250 kPa s m-2 1000
100
10
1 -100
0
100
200
300
400
500
600
700
800
Time, µsec
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30
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Viscosity correction function In the case of a porous medium with a KNOWN pore size distribution e(s) we can use the Biot’s VCF to predict the characteristic acoustic impedance and complex wavenumber: ∞
F (ω ) ∝
∫ τ (ω )e(s)ds
0 ∞
total shear stress on pore walls
,
∫ U (ω )e(s)ds
(1) average seepage velocity
0
Commonly, the function e(s) is substituted with its log-normal fit, f(s), so that simple approximations to the integrals in exp. (1) can be derived (e.g. [K.V.Horoshenkov et al, JASA, 104, 1198-1209 (1998)]) If Pade approximation fails, an alternative can be 1.
Interpolate the experimental data on the cumulative pore size distribution
2.
Numerically differentiate the result to obtain the experimental PDF e(s)
3.
Carry out direct numerical integration of exp. (1)
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COUSTONE (Flint mixed with epoxy resin binder) R = 31.5 kPa s m-2, Ω =0.40, q2= 1.66, h = 21mm
10mm
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The normalised surface impedance of a 20 mm layer of Coustone (predicted from the pore size distribution data)
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What are common complications in modelling acoustic properties of porous media?
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Loose granular media in different compaction states
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Effect of particle size 40m m thick layer
Sound absorption coefficient
1.0
10 from F. Sgard and X. Olny, Appl. Acoust., 66(6), 2005.
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Homogenisation procedure for double-porosity media Porosity Dynamic density
Ω db = Ω p + (1 − Ω p )Ω m
ρ db = {(1 − Ω) / ρ m + 1/ ρ p }
Complex compressibility
−1
Cdb = {C p + (1 − Ω p )Cm }
The key point is linked to the fact that the wavelength in the microporous domain should be of the same order of magnitude as the mesoheterogeneities, i.e. the characteristic frequency of pressure diffusion effects is carefully chosen characteristic frequency of pressure diffusion effects
ωd = ωv
(1 − Ω p ) P0 ρ 0 qm2 D (0)Ω R 2 m
2 m
characteristic viscous frequency
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Effect of double porosity (macro-perforation) on absorption properties
from [Sgard and Olny, Appl. Acoust., 66(6), 2005].
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A realistic double porosity structures developed at Bradford
~7mm
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Finally! Effect of frame vibration
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Measured absorption coefficient of G10 plates 500mmx500mm and 90mm with 80 mm air gap
[Swift and Horoshenkov], JASA 107, 1786-1789 (2000).
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Basic equations
Biot coupling coefficient
loss coefficient
P. Leclaire, K. V. Horoshenkov, et al, JSV 247 (1): 19-32 (2001).
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Predicted effect of material density on the averaged absorption coefficient (a 10mm thick plate 80 mm from rigid impervious wall)
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THANKS FOR YOUR ATTENTION
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