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

7-1-2013

The Influence of Boundary Conditions andConstraints on the Performance of Noise ControlTreatments: Foams to MetamaterialsJ Stuart BoltonPurdue University, bolton@purdue.edu

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Bolton, J Stuart, "The Influence of Boundary Conditions and Constraints on the Performance of Noise Control Treatments: Foams toMetamaterials" (2013). Publications of the Ray W. Herrick Laboratories. Paper 82.http://docs.lib.purdue.edu/herrick/82

J. Stuart BoltonRay. W. Herrick LaboratoriesSchool of Mechanical EngineeringPurdue University

RASD 2013, Pisa, Italy, July, 2013

Effect of front and rear surface boundary conditions on foam sound absorption

Influence of edge constraints on transmission loss of poroelastic materials including effect of finite mass supportssupports

“Metamaterial” Barrier

2

3

Normal Incidence Measurement Normal Incidence Measurement f flf flof Reflectionof Reflection

4

FilmFilm--faced Polyurethane Foamfaced Polyurethane Foam

Scanning electron micrographs of the foam sample

• 25 mm layer of foam – one side covered with flame‐bonded film, the other open.

• Many intact membranesMany intact membranes

5

Reflection Impulse ResponseReflection Impulse Response

(Film-faced surface up) (Foam-open surface up)

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OneOne--Dimensional Dimensional PoroelasticPoroelasticM i l ThM i l ThMaterial TheoryMaterial Theory

Equations of motion:Fluid:

Solid:

Based on Zwikker and Kosten, plus Rosin with complex density and air ff k f b hstiffness taken from Attenborough.

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Boundary ConditionsBoundary Conditions

Open foam surface Foam surface sealed with an i i b

Foam fixed to a hard backingimperious membrane

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Reflection Impulse Response Reflection Impulse Response --p pp pPredictedPredicted

Film-faced FoamOpen Surface Foam

Reflection from rear surface Disaster!

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FilmFilm--faced Foam / Thin Air Gapfaced Foam / Thin Air Gap/ p/ p

Impedance:

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FilmFilm--forced Foam / Thin Air Gapforced Foam / Thin Air GapFilmFilm forced Foam / Thin Air Gapforced Foam / Thin Air Gap

1600 Hz350 Hz

1600 Hz

Inverted reflection from rear surface

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Rear Surface Boundary ConditionsRear Surface Boundary Conditions25mm foam layer with bonded membrane

1. No Airspace:

2. Airspace:p

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membranefoamo Bonded/Bondedbacking

/

o Bonded/Unbondedairspace

o Bonded/Unbonded

b d d d do Unbonded/Bonded

o Unbonded/Unbonded

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Normal Incidence AbsorptionNormal Incidence Absorptionpp

o Foam  – 25 mm, 30kg/m3

o Membrane   – 0.045 kg/m2

o Airspaces   – 1 mm

Effects of Airspace at front and rear

1. Film/Foam/Backing   

2. Film/Space/Foam/Backing

3. Film/Foam/Space/Backing

Effects of Airspace at front and rear

/ / p / g

4. Film/Space/Foam/Space/Backing

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Impedance Tube TestingImpedance Tube TestingMelamine Foam (8.6 kg/m3)

100 mm diameter

p gp g

100 mm diameter 25 mm thick

Each sample fit exactly by trimming the diameter & checking the p y y g gfit with a TL measurement

Two Facing & Two Rear Surface Boundary Conditions

Multiple trials Multiple samples

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Sample Fit: TL QualificationSample Fit: TL Qualificationp Qp Q

N Z TL S l

Transmission Loss

Non‐Zero TL = Sample Constrained As‐Cut

1st Trim

2nd Trim

3rd Trim

Zero TL = Sample Free to Move 4th Trim

No Leakage

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Surface ConfigurationsSurface Configurations

Front Surface: Rear Surface:

gg

1 2 1 2

Loose Glued Gap Fixed

1) Plastic film near, but not adhered to foam

1) Small gap between foam & rigid wall

) dh d d2) Plastic film glued to foam

2) Foam adhered to rigid wall

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Absorption vs. Configuration Absorption vs. Configuration -- TestTest

Absorption Coefficient Loose - Gap

-- TestTest

Loose - Fixed

Gl d GGlued - Gap

Glued-Fixed

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Helmholtz Resonator EffectHelmholtz Resonator Effect

??

M h i l I dMechanical Impedance

Mass

StiffStiffness

Total Acoustic Impedance

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Helmholtz Resonator EffectHelmholtz Resonator Effect

??

Combined Foam + Helmholtz Resonator System is Similar to

Measured System

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Helmholtz Resonator EffectHelmholtz Resonator Effect

??But is it really due to edge gaps?

Measured GluedF i Fi dFacing + Fixed

with Edge Sealed

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22

Resting on Floor Bonded to Backing

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Tensioned Tensioned MembranesMembranesModelModel VerificationVerification –– Velocity MeasurementVelocity MeasurementModel Model Verification Verification –– Velocity MeasurementVelocity Measurement

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Model Verification Model Verification –– Vibrational Vibrational ModesModesModesModes

Theory ExperimentAbsolute velocity of membrane - Experiment

1st 0.5

1

p|/|v

/p|m

ax

-0.050

0.05

-0.050

0.050

xy

|v/

2nd

26

Model Verification Model Verification –– Experiment Experiment SetSet--upupSetSet--upup

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Model Verification Model Verification –– Model Model OptimizationOptimizationOptimizationOptimization

o Given experimental results as input Find appropriate materialinput, Find appropriate material properties (To , ρs , η )

Why this behavior? – Finite size, held at edge, finite stiffness.

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Glass Fiber Material Inside of Glass Fiber Material Inside of Sample HolderSample HolderSample HolderSample Holder

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Anechoic Transmission Loss Anechoic Transmission Loss (Green)(Green)(Green)(Green)

35

40Experiment FE Prediction (Edge constrained)Prediction (Unconstrained case)

25

30

15

20

TL (d

B)

5

10

15

Increase in TL due to edge constraint

102 103 1040

5

F (H )

(10dB)Shearing mode

Frequency (Hz)

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PoroelasticPoroelastic Material Properties Material Properties Used in CalculationsUsed in CalculationsUsed in Calculations Used in Calculations

MaterialBulk

density

(Kg/m3)

Porosity TortuosityEstimated flow

resistivity

(MKS Rayls/m)

Shear modulus

(Pa)

Loss factor

Yellow

Green

6.7

9.6

0.99

0.99

1.1

1.1

21000

31000

1200

2800

0.350

0.275

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Variation of Shear ModulusVariation of Shear Moduluso As shear modulus increases, the minimum location of TL moves to

higher frequencies

30

35

40Shear M odulus = 1000 PaShear M odulus = 2000 PaShear M odulus = 3000 PaShear M odulus = 4000 Pa

20

25

30

L (d

B)

10

15

TL

102 103 1040

5

Frequency (Hz)Frequency (Hz)

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Variation of Flow ResistivityVariation of Flow Resistivity

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• Flow resistivity controls TL at low and high frequency limit

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F low res is t ivity = 10000 M K S R ay ls /mF low res is t ivity = 20000 M K S R ay ls /mF low res is t ivity = 30000 M K S R ay ls /mF low res is t ivity = 40000 M K S R ay ls /m

20

25

TL (d

B)

1 0

15

10 2 10 3 10 40

5

F requenc y (H z )

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Investigation of Vibrational Investigation of Vibrational Modes of Glass Fiber MaterialsModes of Glass Fiber MaterialsModes of Glass Fiber MaterialsModes of Glass Fiber Materials

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Vibrational Modes of Fiber Glass Vibrational Modes of Fiber Glass Materials (1st and 2nd Modes Green)Materials (1st and 2nd Modes Green)Materials (1st and 2nd Modes, Green)Materials (1st and 2nd Modes, Green)

ExperimentFEM

0

0.5

1

(a)

|vf/p

|/|vf

/p|m

ax

0

0.5

1

(b)

|vf/p

|/|vf

/p|m

ax

1st

-0.05

0

0.05

-0.05

0

0.050

xy -0.05

0

0.05

-0.05

0

0.050

xy

(133 Hz)

0.5

1

(c)

|/|vf

/p|m

ax

0.5

1

(d)|/|

vf/p

|max

2nd

-0.05

0

0.05

-0.05

0

0.050

xy

|vf/p

|

-0.05

0

0.05

-0.05

0

0.050

xy

|vf/p

|2nd

(422 Hz)

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Internal Constraint to Enhance Internal Constraint to Enhance the Sound Transmission Lossthe Sound Transmission Lossthe Sound Transmission Loss the Sound Transmission Loss

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Sound Transmission Loss Sound Transmission Loss ((Experiment GreenExperiment Green)) [Density of[Density of PlexiglassPlexiglass: 1717 Kg/m3]: 1717 Kg/m3]((Experiment, GreenExperiment, Green)) [Density of [Density of PlexiglassPlexiglass: 1717 Kg/m3]: 1717 Kg/m3]

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Effect of Releasing the Internal Effect of Releasing the Internal CrossCross-- Constraint (Measurement)Constraint (Measurement)CrossCross Constraint (Measurement)Constraint (Measurement)

Cardboard25

30

CardboardConstraint

5

10

15

20

TL(

dB)

30

35

40

(b)

102 1030

PlexiglassConstraint10

15

20

25

30

TL

(dB)

102 1030

5

F requenc y (H z)

Relatively heavy constraint required to realize Relatively heavy constraint required to realize low frequency benefit.

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Effect of Releasing the Internal Effect of Releasing the Internal CrossCross Constraint (FEM Prediction)Constraint (FEM Prediction)CrossCross-- Constraint (FEM Prediction)Constraint (FEM Prediction)

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C db d

5

10

15

20

25

TL

(dB)

CardboardConstraint

102 1030

5

35

40

(b)

15

20

25

30

TL

(dB) Plexiglass

Constraint

102 1030

5

10

F requenc y (H z)

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MetamaterialsMetamaterialso Metamaterials are artificial materials engineered to have properties that may not be 

found in nature. Metamaterials usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior.composition, using small inhomogeneities to create effective macroscopic behavior.

From  :  Meta‐Material Sound Insulation by E. Wester, X. Bremaud and B. Smith, Building Acoustics, 16 (2009)

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Proposed MassProposed Mass--Neutral MaterialNeutral MaterialHomogenized mat.

Cellular panel

MM f 2 cnL

≡

: fff fe eMM f

0

0

22 2

20logeff

cTc j f

STL

M f

T

Frame (Mat. A)

: Mass per unit area: Sound Transmission Loss

eff

STLM

Plate (Mat. B)

Unit cellnL L

LL Cellular material with a periodic array of unit cells

Unit cell has components with contrasting mass and moduli

Characteristics of infinite, periodic panel are same as that Characteristics of infinite, periodic panel are same as that of a unit cell for normally incident sound 

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Low Frequency EnhancementLow Frequency Enhancement

A clamped plate has high STL at very low frequencies due to the effect of boundary conditions and finite size and stiffness.

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MaterialMaterial--Based Mass ApportioningBased Mass ApportioningMaterialMaterial Based Mass ApportioningBased Mass Apportioning Each unit cell

Overall mass constant iff i l f f d l Different materials for frame and plate

A series of cases for μ between  0.1 and 10000 ρp and ρf variedρp ρf Ef varied keeping Ep constant so that

Mat. A

f p f pE E

Mat. B

Base unit cell Cellular unit cellBase unit cell Cellular unit cell

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Experimental ValidationExperimental Validationo A good qualitative agreement is observed 

between measurements and FE predictions

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MaterialMaterial--Based Mass ApportioningBased Mass Apportioningpp gpp g As µ↑

High STL region broadens in the low frequency regime

Region between the first peak and dip is widening Region between the first peak and dip is widening

The dip – being shifted to the right – desirable

→O(100)→ t t µ→O(100)→saturates

Ep = 2 GPa

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Effective Mass as a Function of FrequencyEffective Mass as a Function of FrequencyEffective Mass as a Function of FrequencyEffective Mass as a Function of Frequency Magnitude of Meff higher than space‐averaged areal mass 

in the range of 0‐1000 Hz

A d f it d hi h i 800 1000 H An order of magnitude higher in 800 – 1000 Hz range

Shows strong negative mass effect in the peak STL region

02 cT 02 2 effc j fM f

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Mechanism Behind High STLMechanism Behind High STL

o Averaged displacement phase  switches from negative to positive value at the STL peakpositive value at the STL peak

o Parts of the structure move in opposite directions—similar to observations in LRSMs—resulting in zero averaged displacement 

o “Negative mass” observed without locally resonant elements

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Hybrid MaterialHybrid Material

o Cellular structure increases STL at low frequencies

o Lightweight, fine fiber fibrous layer can be used to recover performance at higher frequencies

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Hybrid MaterialHybrid MaterialLow Sound Speed Front Metamaterial Core Fibrous Cell Filling

Directs non‐normally  Locally resonant core Fibrous cell fillingincident sound to core

Locally resonant core gIncreases STL at high Hz

o Predicted Sound Transmission Loss in Hybrid System with Fibrous Cell Filling

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• Front and rear boundary conditions have a profound effect on the sound absorption 

offered by poroelastic materialsoffered by poroelastic materials

• Those effects are predictable and measureable

• Internal constraint of poroelastic materials can increase their transmission loss, but 

finite weight of required supports should be accounted for

•Metamaterials for transmission loss typically depend on the presence of constraints, 

geometry and flexural stiffness for their performance

• A proposed mass‐neutral “metamaterial” barrier featuring spatially‐periodic internal 

constraints gives low frequency advantage with respect to the mass law but wouldconstraints gives low frequency advantage with respect to the mass law, but would 

require supplementary material to mitigate performance loss at high frequencies

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Former Students:• Edward R. Green

• Bryan H. Song

• Jinho Song

• Ryan Schultz

Current Students:y

• Srinivas Varanasi

• Yangfan Liu

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pp 3 11: J Stuart Bolton Ph D Thesis University of Southampton 1984 Cepstral techniques in the• pp.  3–11:  J. Stuart Bolton, Ph.D. Thesis, University of Southampton, 1984. Cepstral techniques in the measurement of acoustic reflection coefficients, with applications to the determination of acoustic properties of elastic porous materials.

• pp. 12‐14:  J. Stuart Bolton, Paper DD4 presented at 110th meeting of the Acoustical Society of America, Nashville TN, November 1985.  Abstract published in the Journal of the Acoustical Society of America 78(S1) S60. Normal incidence absorption properties of single layers of elastic porous materials.

• pp. 15‐21: Ryan Schultz and  J. Stuart Bolton, Proceedings of INTER‐NOISE 2012, New York City, 19‐22 August, 2012.  Effect of solid phase properties on the acoustic performance of poroelastic materials.

• pp. 25‐28: Jinho Song and J. Stuart Bolton, Proceedings of INTER‐NOISE 2002, paper N574, 6 pages, Dearborn, Michigan August 2002 Modeling of membrane sound absorbersMichigan, August 2002. Modeling of membrane sound absorbers.

• pp. 29‐33: Bryan H. Song,  J. Stuart Bolton and Yeon June Kang, Journal of the Acoustical Society of America, Vol. 110, 2902‐2916, 2001. Effect of circumferential edge constraint on the acoustical properties of glass fiber materials.

• pp. 34‐35: Bryan H. Song, and J. Stuart Bolton,  Journal of the Acoustical Society of America, Vol. 113, 1833‐1849, 2003. Investigation of the vibrational modes of edge‐constrained fibrous samples placed in a standing wave tube.

• pp. 36‐39: Bryan H. Song and J. Stuart Bolton, Noise Control Engineering Journal, Vol. 51, 16‐35, 2003. Enhancement of the barrier performance of porous linings by using internal constraints.

• pp. 42‐49: Srinivas Varanasi, J. Stuart Bolton, Thomas Siegmund and Raymond J. Cipra, Applied Acoustics, Vol. 74, 485 495 2013 The low frequency performance of metamaterial barriers based on cellular structures485‐495, 2013. The low frequency performance of metamaterial barriers based on cellular structures.

• See also: J. Stuart Bolton and Edward R. Green, Paper E4 presented at 112th meeting of the Acoustical Society of America, Anaheim CA, December 1986.  Abstract published in the Journal of the Acoustical Society of America80(S1), p. S10.  Acoustic energy propagation in noise control foams:  approximate formulae for surface normal impedance. 

• Presentations available at:  http://docs.lib.purdue.edu/herrick/

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