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1
Acoustic Porous Materials and Their Characterisation
Kirill V. Horoshenkov
School of Engineering, Design and Technology
University of Bradford
BradfordK.Horoshenkov@bradford.ac.uk
2
Where is Bradford on the map?
Bradford city
Yorkshire dales
3
Acoustic Research at Bradford University
• Acoustic materials (Prof. Horoshenkov, Dr. Swift (Armacell UK))
• General sound propagation (Prof. Horoshenkov, Prof. Hothersall*, Dr. Hussain)
• Environmental noise (Prof. Watts (TRL), Prof. Hothersall*, Prof. Horoshenkov)
• Vibration (Prof. Wood, Prof. Horoshenkov)
supported by ~15 PhD/MPhil students
(*) – visiting professor
4
Experimental Facilities at Bradford University• Sound propagation experiments
• Extensive experimental setup for characterisation of material
pore structure
• Extensive experimental setup for measuring acoustic, vibration
and structural performance of poro-elastic materials
• Facilities for poro-elastic material manufacturing
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Topics of Research on Acoustic Materials
• Development of improved prediction models
• Experimental investigation of porous media
• Development of novel, environmental sustainable materials with
improved acoustic efficiency
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Where these materials are actually used?
7
Pipeline insulation
Automotive insulation Aircraft insulation
Noise from electronic cabinets
8
How these materials look like?
9
Granular mixConsolidated recycled foam
Re-constituted foam grainsVirgin reticulated foam
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What they actually do to sound?
11
Effect on room responsePropagation in empty enclosure
with rigid walls
micspeaker
Propagation in enclosure with porous layer
12
Effect on pipe response(20m long, 600mm concrete pipe)
13
How these materials are characterised?
14
Impedance tube method BS 10534-2
pr
pi
Sound source
Stationary random noise
∆
p2p1
Rigid backing
l
mic
roph
one
2
tested sample
++
==∆−∆
RRee
ppH
ikik
1)(
1
2ω iklik
ik
eHe
eHR 2
)()()(
−−
= ∆−
∆
ωωω
mic 3
mic
roph
one
1
15
Measuring frequency-dependent dynamic stiffness
top accelerometer
loading plate (m)
tested sample (Z, k)
impedance head
kZE ω
=klTklMZ
cossin
−=
ω
( )2
1 1cos mT Mk lm M T
− − + = + shaker
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Armafoam sound
1.00E+05
1.00E+06
10 100 1000
frequency, Hz
Rea
l
17
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
10 100 1000
Frequency (Hz)
Loss
fact
or
18
bottom accelerometer
tested sample
Measuring dynamic stiffness to BS29052
loading plate
top accelerometer with dynamic mass
shaker
20 [ / ]s m Pa mω=
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Dynamic Stiffness - BS29052
-60
-55
-50
-45
-40
-35
-30
-25
-20
10 100 1000frequency (Hz)
Rel
ativ
e ac
cele
ratio
n le
vel,
[dB
]
Material 1Material 2
Material 3
lower stiffnes
0f
20
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
-65
-55
-45
-35
-25
-15
-5
5
10 10 0 10 0 0
Frequency, Hz
Tran
smis
sion
Los
s, d
B
With skins on
Without skins
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Airborne transmission loss (99mm sample)
23
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Impact sound insulation
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Octave -band level
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
10 100 1000 10000
frequency, Hz
Rel
ativ
e ac
cele
ratio
n le
vel,
dB. R
e. 1
V
Developed sample
Cumulus
Without material onw ooden base
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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 = 0Comparison of some common impedance models. Semi-infinite layer
1
10
100
1000
10000
100000
1000000
-100 0 100 200 300 400 500 600 700 800
Time, µsec
Res
pons
e to
a δ
-pul
se
Pade approximation
Keith Wilson (A-C-like)
Miki model
Delany and Bazley model
R = 250 kPa s m-2
non-analytic models
analytic models
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31
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Viscosity correction function
,)()(
)()()(
0
0
∫
∫∞
∞
∝dsseU
dsseF
ω
ωτω
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:
total shear stress on pore walls
(1)
average seepage velocity
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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10mm
COUSTONE (Flint mixed with epoxy resin binder)R = 31.5 kPa s m-2, Ω =0.40, q2= 1.66, h = 21mm
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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?
36
Loose granular media in different compaction states
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Effect of particle size
40mm thick layer
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
100 1000 10000
Frequency, Hz
Soun
d ab
sorp
tion
coef
ficie
nt
<0.15 mm
0.15-0.50 mm
0.50-0.71 mm
0.71-1.00 mm
1.40-2.00 mm
2.00-2.36 mm
2.36-3.50 mm
3.50-5.00 mm
greater particle size
38
• the degree of compaction
• viscous effects
• microporosity
• particle friction.
These parameters are directly measurable in-situ and can account
phenomenologically for:
A general and more simple method is to relate empirically the acoustic properties of a loose granular mix to the following parameters:
• characteristic dimension of the particles
• porosity
• specific density of the grain base.
Criteria for improved model for loose granulates
39
An improved semi-empirical model
40 10D cρχη
−=
density of airsound speed
characteristicparticle dimension
1. Relates the characteristic dimension of the particles and accounts for the viscous effects in the porous structure via
dynamic viscosity
2. Accounts phenomenologically for the particle micro-porosity and frame vibration effects via
0310 ρρ gM =
specific density ofgains
40
Acoustic Properties
It can be shown that the characteristic impedance (W) and propagation constant (γ) can be expressed empirically
( , , )W f Q Mχ=
( , , )g Q Mγ χ=
and some analytical functions
where the structural characteristic is also predicted empirically by
20.2(1 )(1 )QkDχ
−Ω +Ω=
Ωwavenumber
porosity
41
Results for real part of characteristic impedance
Voronina and Horoshenkov, Appl. Acoust., 65, 673-691 (2004)
acoustic resistance
42
Results for real part of propagation constant
Voronina and Horoshenkov, Appl. Acoust., 65, 673-691 (2004)
43
Effect of moisture
funnel
tested sample
44
Effect of moisture on the impedance of a50mm water-saturated layer of fine sandResistance
200 300 400 500 600 700 800 900 1000 1100 1200 13000
20
40
60
80
100
120
140
Frequency, Hz
|zs|
S = 0% S =13%
S = 19%
S = 29%
S = 48%
S = 72%
S = 94%
45
Effect of double porosity (macro-perforation)
macro-poresmicro-porousframe
/ 10p ml l >from F. Sgard and X. Olny, Appl. Acoust., 66(6), 2005.
46
Homogenisation procedure for double-porosity media
(1 )db p p mΩ = Ω + −Ω Ω
1(1 ) / 1/db m pρ ρ ρ
−= −Ω +
Porosity
Dynamic density
(1 )db p p mC C C= + −ΩComplex compressibility
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
20 02 2
(1 )1
(0)p md
v m m
P qD R
ρωω
−Ω=
Ω
characteristic frequency of pressure diffusion effects
characteristic viscous frequency
47
Effect of double porosity (macro-perforation) on absorption properties
from [Sgard and Olny, Appl. Acoust., 66(6), 2005].
48
A realistic double porosity structures developed at Bradford
~7mm
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Finally!
Effect of frame vibration
50
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
loss coefficientBiot coupling 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)
53
THANKS FOR YOUR ATTENTION
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