Porous Materials for Sound Absorption and Transmission Control

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Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering

8-2005

Porous Materials for Sound Absorption andTransmission ControlJ Stuart BoltonPurdue University, [email protected]

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Porous Materials for Sound Absorption and Transmission

ControlControl

J. Stuart BoltonRay W. Herrick Laboratories

P d U i itPurdue University

Introduction

What are Porous Media? Two phases Two phases

Solid Fluid

Wh t d th d ? What do they do? Convert organized acoustical motion into heat

Dissipation of Energy

What don’t they do? Bl k d i t ll f l b i

Dissipation of Energy

Block sound : i.e., not usually useful as barriers(by themselves)

Purdue University Herrick Laboratories

Introduction

Dissipation mechanisms Viscous Viscous Thermal Structural

Examples of porous materials Glass fiber Mineral wool Mineral wool Open or partially open cell foams

Applications Automotive, Aircraft, …


SEM – Glass Fiber


SEM – Resinated Glass Fiber


SEM – Partially Reticulated Foam


SEM – Shoddy


SEM – Thinsulate


Sound Propagation in Porous Media

P M t i l Porous Materials

Two phases: Solid (frame) and gas (air) Allow two longitudinal wave types which appear in

both phases Allow transverse wave motion if frame possesses p

shear stiffness Display large sensitivity to boundary conditions if

frame is relatively stiff (modulus near that of air)


Transmission Measurements

Test signal: Linear Frequency Sweep 0 Hz 25Frequency Sweep, 0 Hz-25 kHz, 20 ms

Sample Rate: 100 kHz Resolution: 12 bits Post-Acquisition: Re-

sample to 50 kHz


Foam Impulse Response

Note: Frame Wave- first arrival


Absorption treatments

Bonded/Bonded membranefoam

Bonded/Unbonded

backing

Unbonded/Bonded

airspace

Unbonded/Unbonded


Normal Incidence AbsorptionEffects of Airspace at front and rear

1. Film/Foam/Backing 2. Film/Space/Foam/Backing3 Fil /F /S /B ki3. Film/Foam/Space/Backing4. Film/Space/Foam/Space/Backing

Foam – 25 mm, 30kg/m3

MembraneMembrane – 0.045 kg/m2

Airspaces – 1 mm


Ch t i ti f P M diCharacterization of Porous Media

Rigid

Solid phase does not move Solid phase does not move Frame bulk modulus significantly greater than that of air Airborne wave only

*situations in which frame is not excited directly Porous ceramics Sintered metals



Limp

Solid phase moves – driven by fluid motion onlySolid phase moves – driven by fluid motion onlyFrame bulk modulus significantly less than of airAirborne wave onlyLimp glass fibers, thinsulate and other fibrous media



Elastic

Solid phase movesSolid phase movesFrame bulk modulus of same order of that as airAirborne, frame and shear wavesB d diti i t tBoundary conditions are very importantPolyurethane and polyimide foams


Physical Properties of Porous Media

Acoustical properties are determined by macroscopicphysical properties.p y p p

- Flow resistivity- porosity Fluid-acoustical

t

gid

p - pore tortuosity- Bulk density- In vacuo bulk modulus

Sh d l

parametersRi

Lim

p

Ela

stic

- Shear modulus- Loss factor

With knowledge of these properties the acoustical

Elastic properties

E

With knowledge of these properties the acoustical performance of porous media can be predicted.



Flow Resistivity

Resistance to steady state flow through a porous material

Determined by- pore tortuosity- viscous drag

When pores are “straight”, measure of viscous dissipation potential


Measurement of Physical Properties- Flow Resistivity



Tortuosity

M f d i ti f f t i ht li th h Measure of deviation of pore from straight line through material

Ratio of actual path length through material to linear path lengthpath length

Results in inertial coupling between solid and fluids phases

Ranges from 1 (low density fibrous material) to 10 Ranges from 1 (low density fibrous material) to 10 (partially reticulated foam)


Modeling of Porous Media Objective Material

Microstructure

MacroscopicProperties

Limited

FundamentalAcoustic

Well Developed

Properties

Installed

Analytical Well Developed

Numerical Initial Work

InstalledAcoustic

Properties


Microstructure to Macrostructure For fibrous media made up of mono-diameter fibers

(e.g., from Beranek, Noise and Vibration Control)


Modeling of Porous MediaApproach followed by Bolton and Allard Based on theory of elastic porous materials by Biot (1956):

Allo s trans erse a e motion- Allows transverse wave motion- Expressed in very general form- Most widely used in geophysics

H Here:- Adapt theory to “acoustic” porous materials (i.e., foam and glass fiber)- Express in terms of conventional variables (i.e., displacement and

pressures)pressures)- Derive boundary conditions applicable to typical reflection and

transmission problems Results: Results:

- First theory capable of predicting oblique incidence behavior of foam in noise control application


Theoretical Approach WRITE:

- stress-strain relations for each phase- stress strain relations for each phase- Dynamic relations for each phase

COMBINE TO YIELD TWO WAVE EQUATIONS:V l t i t i- Volumetric strain

- Rotational strain FROM SOLUTIONS DERIVE:

- Displacement fields- Normal and shear stresses at boundaries

DETERMINE COMPONENT AMPLITUDES: DETERMINE COMPONENT AMPLITUDES:- By application of boundary conditions


Notation

Forces acting on solid phase/unit material area:

Forces acting on fluid phase/unit material area:

1. s = - hP, where h=porosity2. Solid displacement denoted by ū3. Fluid displacement denoted by Ū

* Notes:


The RAYLEIGH Model

The original model The modified model (allowing f t t it )for pore tortuosity)


Fluid-Structural Coupling Inertial – proportional to relative acceleration

Viscous – proportional to relative velocity


Dynamic Relations

)()()1( 2

22

22

2

1 yyyyyxyy Uu

tbUu

tq

tu

xy

Solid:yyyy tttxy

)()()1(2

22

y uUbuUqUs

Fluid: )()()1( 2222 yyyy uU

tbuU

tq

ty

where = bulk density of framewhere ρ1= bulk density of frameρ2=ρ0h (bulk fluid density)q2 = structure factor (inertial coupling)q structure factor (inertial coupling)b = viscous coupling factor

* Note : Viscous and inertial coupling


Wave Equations

Volumetric Strains: 024 BeeAe

Solution of form: xjkCe 2,1

Where:

242

22,1

BAAk

Note: two longitudinal wave types distinguished by different wave numbers: i.e.,

2

Airborne wave Frame wave


Wave Equations

Rotational Strains: 022 tk Rotational Strains:

Solution of form: xjktCe

0 ztz k

Where: ωz = z-component of

Ce

kt = transverse wave wave number

Note: single transverse wave typeNote: single transverse wave type


Phase Speed and Attenuation

Phase Speed Attenuation


Forms of Solutions

xjkyjkyjkyjkyjk xyyyy eeCeCeCeCe ][ 22114321

xjkyjkyjk xtyty eeCeC ][ 6 z eeCeC ][ 65

222,12,1 xyy kkk 22

xtty kkk where: and

xyxxxyxx tltltltlz UUUUuuuu ,,,,,,,,,

xyy s ,,Then derive:

and


Forms of Solutions Solid Displacement:

11 kk yjkyyjkyxjk

221

112

1

1 11 Cek

Cek

jeu yjkyyjkyxjky

yyx

22 kk jkjk

Longitudinal

422

232

2

2 22 Cekk

Cekk yjkyyjky yy

k yjkyjkxjk

t

x tytyx eCeCekkj 652 Transverse

Similar expression for U σ τ etc all in terms of six unknownSimilar expression for Uy,σy,τxy, etc., all in terms of six unknown constants C1-C6; they are determined by application of the boundary conditions.


Sound Transmission Through Double Panels

Approach: Substitute allowed solutions into boundary conditions. Arrange as matrix problem in wave amplitudes and

solve for required coefficients.


Boundary Conditions Open Surface:

1. Volume Velocity: vy = iω [ (1-h) uy + h Uy ]2. Fluid Force: - h p = sp3. Solid Force: - (1-h) p = σy

4. Shear Force: τxy = 0


Boundary Conditions Bounded Euler-Bernoulli Plate (D, ms):

1. Normal Velocity: vy = iω W2. Solid Displacement: uy = W3 Fluid Displacement: U = W3. Fluid Displacement: Uy W4. Tangential Displacement: ux = - (h1/2) ∂W/∂x

5. Eqn. of Motion: hpsWmWD xy

)( 1

24

Note: 1. transverse wave excitation through 2-5.2. plate thickness affects coupling.

xps

tm

xD ys

2

)(24


2. plate thickness affects coupling.

Absorption treatments

Bonded/Bonded membranefoam

Bonded/Unbonded

backing

Unbonded/Bonded

airspace

Unbonded/Unbonded


Normal Incidence AbsorptionEffects of Airspace at front and rear

1. Film/Foam/Backing 2. Film/Space/Foam/Backing3 Fil /F /S /B ki3. Film/Foam/Space/Backing4. Film/Space/Foam/Space/Backing

Foam – 25 mm, 30kg/m3

MembraneMembrane – 0.045 kg/m2

Airspaces – 1 mm


Sound Absorption Treatments

Owing to high impedance frame waves

1. “Loose” surface membrane yields better overall sound absorption than bonded membrane (with exception of very low frequencies)very low frequencies).

2. Small airspace (~ 1 mm) behind foam layer enhances low frequency performance with or without front membrane.

3. Light, loose membrane on foam with thin backing space gives performance as good as unfaced foamspace gives performance as good as unfaced foam while protecting foam.


Sound Transmission Through Double Panels

Approach:Approach: Substitute allowed solutions into boundary conditions. Arrange as matrix problem in wave amplitudes and solve

for required coefficientsfor required coefficients


Transmission Loss Measurements

Procedure Procedure

- Measure 1/3 octave mean square pressure in source room ( Ii )source room ( Ii )- Measure 1/3 octave transmitted intensity averaged over panel area ( It )( It )- TL = 10 log ( Ii / It )


Test Panel Mounting


Foam Mounting

• Note: Panel Dimensions – 1.2 m by 1.2 m


Panel Configurations Tested

Foam:30 kg/m3 – 26 mm thick

Panel: Panel:Aluminum – 0.05” and 0.03” thick

Panel Separation:26 mm to 41 mm


Transmission LossTheory

Experiment Double Panel: Lined - 0.05” & 0.03”

• Foam UNBONDED to incident side panel


p

Transmission LossTheory

Experiment Double Panel: Lined - 0.03” & 0.05”

• Foam BONDED to both panels


p

Transmission Loss Double Panel: Lined - 0.03” & 0.05”


Sound Transmission

High impedance frame wave causes performance to depend on mountingto depend on mounting.

Avoid direct excitation of frame waves- do not continuously bond foam to backing- do not continuously bond surface treatments to foamfoam

Bonded attachmentShifts “mass-air-mass” resonance to higher frequencies- Shifts mass-air-mass resonance to higher frequencies

- Decreases high frequency transmission loss


Multi-layer models and GUI program

• Develop various combinations of iso. or aniso. foam, stiff panel and air layers. • Implement user-friendly program running as GUI form.

O i iOrganizing by GUI

Aircraft Application

Conventional ribbed-aluminum fuselage Y

Honeycomb core• Different stiffness in X,Y & Z dir.• solid and fluid (air) parts

X

Replaced by

Z

Transversely poro-elastic modeling

Replaced by Nomex honeycomb sandwich Panel Y

• Transversely isotropic properties5 elastic constants : Ex = Ey , Ez ,Gzx ,v xy ,v zx

X

Z

y y

• Porous foam with constants, porosity, bulk density, flow resistivity and tortuosity


TL for 1/2” lined and unlinedFuselage Example

Lined model 80

Lined with 1/2” glass fiber

prediction

measurement60

70

TL(dB)U li d

Unlined model

measurement

40

50

(dB)Unlined- 1/2” air layer

prediction

measurement

20

30

measurement

102 103 1040

10

Frequency (Hz)* About 15dB improvement above 1kHz by lining with ½” fibrous material in the i b t h b l Frequency (Hz)air space between honeycomb panel

and the interior trim.

Finite Element Modeling Practical Treatments


Shape Optimization of Foam Wedge Objective – maximize absorption offered by a wedge

over a specified frequency rangeconstrained edgesrigid piston

f oamair

uo ejt a

hard wallc d

L

xy

- Wedge defined by θ when volume and a is held constant- Given volume find optimum angle, θ

L


p g ,

Shape Optimization of Foam Wedge

0.8 0.

1.0 1.(a)

0.8 0

1.0(b)

0.4 0.4

0.6 0.

= 36o (optimal wedge)

0.4 0

0.6 0

0.0 0.

0.2 0.2

0 500 1000 1500 2000

( p g )

Frequency (Hz)

= 132o

= 180o

0.0 0

0.2 0

16 28 36 41 48 59 74 97 132 180wedge tip angle ()


System Configurations

- In system (b), tortuosity of a foam layer is varied spatially across the duct (in y-direction).


( y )

Sound Transmission Through A Wedge


Sound Transmission Through A Foam Layer Having Spatially Graded Tortuosity


Experimental Setup High Frequency Tube

B & K Type 3560Pulse System





B & K Type 3560Pulse Systemy

(Four Channel)y

(Four Channel)y

(Four Channel)y

(Four Channel)y

(Four Channel)y

(Four Channel)

2.9 cm361.9mKg

Signal AmplifierSignal

GeneratorSignal AmplifierSignal







Generator

A i ti d l fib

7.5 cmMicrophonesMicrophones 134 2MicrophonesMicrophonesMicrophonesMicrophones 134 2MicrophonesMicrophones

Aviation grade glass fiber

AnechoicTermination

AnechoicTermination

AnechoicTermination

AnechoicTermination

Two-MicrophoneImpedance Measurement Tube

B & K Type 4206


B & K Type 4206


B & K Type 4206


B & K Type 4206

NewSampleHolderSampleHolderSampleHolderSampleHolderSampleHolder

AnechoicTermination

AnechoicTermination

AnechoicTermination

AnechoicTermination

AnechoicTermination

AnechoicTermination

AnechoicTermination

AnechoicTermination


B & K Type 4206


B & K Type 4206


B & K Type 4206


B & K Type 4206


B & K Type 4206


B & K Type 4206


B & K Type 4206


B & K Type 4206


NewSampleHolder


AnechoicTermination

AnechoicTermination


B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206B & K Type 4206

Anechoic Transmission Loss

35

40Experiment Prediction using FEM (with edge constraint)Prediction without edge constraint

25

30

Prediction without edge constraint

15

20

TL (d

B)

5

10Increase in TLdue to edge constraint

102 103 1040

Frequency (Hz)

Shearing modeconstraint


Constrained around Edge (50 Hz - 1600 Hz)

35

40ExperimentFEM

25

30

35

15

20

25

TL (d

B)

5

10

15

130 Hz280 Hz

102 1030

5

Frequency (Hz)


Laser Measurement Setup (Large Tube 1” Sample A)(Large Tube, 1 Sample A)

xx

Computer

B & K Type 3560Pulse System(Four Channel) ComputerComputer





B & K Type 3560Pulse System(Four Channel) Computer

d

A

B

d

A

B

Signal AmplifierSignal Signal AmplifierSignal Signal AmplifierSignal Signal AmplifierSignalPolytec FiberOFV 3000C t ll



x2

x1

x2

x1

gGenerator

gGenerator

gGenerator

gGenerator

Sample

Controller

Polytec FiberOFV 511

Fiber interferometer123

gGenerator

gGenerator

gGenerator

gGenerator

Sample

Controller


Fiber interferometer

gGenerator

gGenerator

gGenerator

gGenerator

Sample

Controller


Fiber interferometer123


B & K Type 4206


B & K Type 4206


B & K Type 4206


B & K Type 4206

Plexiglass Two-MicrophoneImpedance Measurement Tube

B & K Type 4206


B & K Type 4206


B & K Type 4206


B & K Type 4206

Plexiglass Two-MicrophoneImpedance Measurement Tube

B & K Type 4206


B & K Type 4206


B & K Type 4206


B & K Type 4206

Plexiglass


The 1st and 2nd Mode Shapes of the Edge-constrained Sample (1”)

1

(a)

ax1

(b)

ax

Edge constrained Sample (1 )FEM Experiment

0.050

0.050

0.5

|vf/p

|/|vf

/p|m

a

0.050

0.050

0.5

|vf/p

|/|vf

/p|m

a

1st Modeat 100 Hz

(c) (d)

-0.05

0

-0.05

0

xy -0.05

0

-0.05

0

xy

at 100 Hz

0.050

0.5

1

|vf/p

|/|vf

/p|m

ax

0.050

0.5

1

|vf/p

|/|vf

/p|m

ax2nd Mode

-0.05

0

0.05

-0.05

0

xy -0.05

0

0.05

-0.05

0

xy

2nd Modeat 350 Hz


Summary

Three types of porous media: rigid, limp and elasticW ti b d l d t l i Wave propagation can be modeled accurately using Biot theory and later variants

Given values for macroscopic parameters, acoustical p p ,behavior of sound absorbing materials can be accurately predicted

Foam finite elements can be used to model arbitrarily Foam finite elements can be used to model arbitrarily-shaped treatments


Future Challenges

Anisotropy – all noise control materials are anisotropicI h it ll i t l t i l Inhomogeneity – all noise control materials are inhomogeneous

Nonlinearity – all noise control materials are nonlineary Inhomogeneous treatments – spatially distributed

properties to improve dissipation Material optimization – especially foams and fibrous

materials Addition of tuned elements to fibersAddition of tuned elements to fibers SEA compatible models


Documents

Porous Materials for Sound Absorption and Transmission Control