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1. Purdue University
Purdue e-Pubs
Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering
7-1-2013
The Influence of Boundary Conditions and
Constraints on the Performance of Noise Control
Treatments: Foams to Metamaterials
J Stuart Bolton
Purdue University, bolton@purdue.edu
Follow this and additional works at: http://docs.lib.purdue.edu/herrick
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for
additional information.
Bolton, J Stuart, "The Influence of Boundary Conditions and Constraints on the Performance of Noise Control Treatments: Foams to
Metamaterials" (2013). Publications of the Ray W. Herrick Laboratories. Paper 82.
http://docs.lib.purdue.edu/herrick/82

2. J. Stuart Bolton
Ray. W. Herrick Laboratories
School of Mechanical Engineering
Purdue University
RASD 2013, Pisa, Italy, July, 2013

3. 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

4. 3

5. Normal Incidence MeasurementNormal Incidence Measurement
f flf flof Reflectionof Reflection
4

6. 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

7. Reflection Impulse ResponseReflection Impulse Response
(Film-faced surface up) (Foam-open surface up)
6

8. OneOne--DimensionalDimensional PoroelasticPoroelastic
M 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.
7

9. Boundary ConditionsBoundary Conditions
Open foam surface Foam surface sealed with an
i i b
Foam fixed to a hard backing
imperious membrane
8

10. Reflection Impulse ResponseReflection Impulse Response --p pp p
PredictedPredicted
Film-faced FoamOpen Surface Foam
Reflection from
rear surface Disaster!
9

11. FilmFilm--faced Foam / Thin Air Gapfaced Foam / Thin Air Gap/ p/ p
Impedance:
10

12. FilmFilm--forced Foam / Thin Air Gapforced Foam / Thin Air GapFilmFilm forced Foam / Thin Air Gapforced Foam / Thin Air Gap
1600 Hz
350 Hz
1600 Hz
Inverted reflection
from rear surface
11

13. Rear Surface Boundary ConditionsRear Surface Boundary Conditions
25mm foam layer with bonded membrane
1. No Airspace:
2. Airspace:p
12

14. membrane
foamo Bonded/Bonded
backing
/
o Bonded/Unbonded
airspace
o Bonded/Unbonded
b d d d do Unbonded/Bonded
o Unbonded/Unbonded
13

15. 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
14

16. Impedance Tube TestingImpedance Tube Testing
 Melamine 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 g
fit with a TL measurement
 Two Facing & Two Rear Surface Boundary Conditions
 Multiple trials
 Multiple samples
15

17. 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
16

18. 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
17

19. Absorption vs. ConfigurationAbsorption vs. Configuration
-- TestTest
Absorption Coefficient Loose - Gap
-- TestTest
Loose - Fixed
Gl d GGlued - Gap
Glued-Fixed
18

20. Helmholtz Resonator EffectHelmholtz Resonator Effect
??
M h i l I dMechanical Impedance
Mass
StiffStiffness
Total Acoustic Impedance
19

21. Helmholtz Resonator EffectHelmholtz Resonator Effect
??
Combined Foam + Helmholtz
Resonator System is Similar to
Measured System
20

22. Helmholtz Resonator EffectHelmholtz Resonator Effect
??
But is it really due to edge gaps?
Measured Glued
F i Fi dFacing + Fixed
with Edge Sealed
21

23. 22

24. Resting on Floor Bonded to Backing
23

26. TensionedTensioned MembranesMembranes
ModelModel VerificationVerification –– Velocity MeasurementVelocity MeasurementModelModel VerificationVerification –– Velocity MeasurementVelocity Measurement
25

27. Model VerificationModel Verification –– VibrationalVibrational
ModesModesModesModes
Theory Experiment
Absolute velocity of membrane - Experiment
1st 0.5
1
p|/|v/p|max
-0.05
0
0.05
-0.05
0
0.05
0
xy
|v/
2nd
26

28. Model VerificationModel Verification –– ExperimentExperiment
SetSet--upupSetSet--upup
27

29. Model VerificationModel Verification –– ModelModel
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.
28

30. Glass Fiber Material Inside ofGlass Fiber Material Inside of
Sample HolderSample HolderSample HolderSample Holder
29

31. Anechoic Transmission LossAnechoic Transmission Loss
(Green)(Green)(Green)(Green)
35
40
Experiment
FE Prediction (Edge constrained)
Prediction (Unconstrained case)
25
30
15
20
TL(dB)
5
10
15
Increase in TL due
to edge constraint
10
2
10
3
10
4
0
5
F (H )
(10dB)
Shearing mode
Frequency (Hz)
30

32. PoroelasticPoroelastic Material PropertiesMaterial Properties
Used in CalculationsUsed in CalculationsUsed in CalculationsUsed in Calculations
Material
Bulk
density
(Kg/m3)
Porosity Tortuosity
Estimated 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
31

33. Variation of Shear ModulusVariation of Shear Modulus
o As shear modulus increases, the minimum location of TL moves to
higher frequencies
30
35
40
Shear M odulus = 1000 Pa
Shear M odulus = 2000 Pa
Shear M odulus = 3000 Pa
Shear M odulus = 4000 Pa
20
25
30
L(dB)
10
15
TL
10
2
10
3
10
4
0
5
Frequency (Hz)Frequency (Hz)
32

34. Variation of Flow ResistivityVariation of Flow Resistivity
40
• Flow resistivity controls TL at low and high frequency limit
30
35
F low res is tivity = 10000 M K S R ay ls /m
F low res is tivity = 20000 M K S R ay ls /m
F low res is tivity = 30000 M K S R ay ls /m
F low res is tivity = 40000 M K S R ay ls /m
20
25
TL(dB)
10
15
10
2
10
3
10
4
0
5
F requenc y (H z )
33

35. Investigation of VibrationalInvestigation of Vibrational
Modes of Glass Fiber MaterialsModes of Glass Fiber MaterialsModes of Glass Fiber MaterialsModes of Glass Fiber Materials
34

36. Vibrational Modes of Fiber GlassVibrational 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|max
0
0.5
1
(b)
|vf/p|/|vf/p|max
1st
-0.05
0
0.05
-0.05
0
0.05
0
x
y -0.05
0
0.05
-0.05
0
0.05
0
x
y
(133 Hz)
0.5
1
(c)
|/|vf/p|max
0.5
1
(d)
|/|vf/p|max
2nd
-0.05
0
0.05
-0.05
0
0.05
0
x
y
|vf/p|
-0.05
0
0.05
-0.05
0
0.05
0
x
y
|vf/p|
2nd
(422 Hz)
35

37. Internal Constraint to EnhanceInternal Constraint to Enhance
the Sound Transmission Lossthe Sound Transmission Lossthe Sound Transmission Lossthe Sound Transmission Loss
36

38. Sound Transmission LossSound 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]
37

39. Effect of Releasing the InternalEffect of Releasing the Internal
CrossCross-- Constraint (Measurement)Constraint (Measurement)CrossCross Constraint (Measurement)Constraint (Measurement)
Cardboard
25
30
Cardboard
Constraint
5
10
15
20
TL(dB)
30
35
40
(b)
10
2
10
3
0
Plexiglass
Constraint10
15
20
25
30
TL(dB)
10
2
10
3
0
5
F requenc y (H z)
 Relatively heavy constraint required to realize Relatively heavy constraint required to realize
low frequency benefit.
38

40. Effect of Releasing the InternalEffect of Releasing the Internal
CrossCross Constraint (FEM Prediction)Constraint (FEM Prediction)CrossCross-- Constraint (FEM Prediction)Constraint (FEM Prediction)
30
C db d
5
10
15
20
25
TL(dB)
Cardboard
Constraint
10
2
10
3
0
5
35
40
(b)
15
20
25
30
TL(dB)
Plexiglass
Constraint
10
2
10
3
0
5
10
F requenc y (H z)
39

41. MetamaterialsMetamaterials
o 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)
40

42. 41

43. Proposed MassProposed Mass--Neutral MaterialNeutral Material
Homogenized mat.
Cellular panel
 MM f 2 c
nL
≡
 : fff fe eMM f
 

 


 
0
0
2
2 2
20log
eff
c
T
c j f
STL
M f
T
Frame (Mat. A)
: Mass per unit area
: Sound Transmission Loss
eff
STL
M
Plate (Mat. B)
Unit cell
nL 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
42

44. 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.
43

45. 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
44

46. Experimental ValidationExperimental Validation
o A good qualitative agreement is observed
between measurements and FE predictions
45

47. 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
46

48. 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 c
T
  02 2 effc j fM f
47

49. 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
48

50. 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
49

51. Hybrid MaterialHybrid Material
Low Sound Speed Front Metamaterial Core Fibrous Cell Filling
Directs non‐normally Locally resonant core Fibrous cell filling
incident sound to core
Locally resonant core g
Increases STL at high Hz
o Predicted Sound
Transmission Loss in Hybrid
System with Fibrous Cell
Filling
50

52. • 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
51

53.  Former Students:
• Edward R. Green
• Bryan H. Song
• Jinho Song
• Ryan Schultz
 Current Students:
y
• Srinivas Varanasi
• Yangfan Liu
52

54. 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 America
80(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/
53