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Acoustic Porous Materials and Their Characterisation

Kirill V. Horoshenkov

School of Engineering, Design and Technology

University of Bradford

BradfordK.Horoshenkov@bradford.ac.uk

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Where is Bradford on the map?

Bradford city

Yorkshire dales

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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

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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?

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Pipeline insulation

Automotive insulation Aircraft insulation

Noise from electronic cabinets

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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?

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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

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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

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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

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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)

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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?

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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

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• 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

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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

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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

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Results for real part of characteristic impedance

Voronina and Horoshenkov, Appl. Acoust., 65, 673-691 (2004)

acoustic resistance

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Results for real part of propagation constant

Voronina and Horoshenkov, Appl. Acoust., 65, 673-691 (2004)

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Effect of moisture

funnel

tested sample

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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%

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Effect of double porosity (macro-perforation)

macro-poresmicro-porousframe

/ 10p ml l >from F. Sgard and X. Olny, Appl. Acoust., 66(6), 2005.

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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

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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

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)

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THANKS FOR YOUR ATTENTION