Purdue University Purdue e-Pubs Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering 7-1-2013 e Influence of Boundary Conditions and Constraints on the Performance of Noise Control Treatments: Foams to Metamaterials J Stuart Bolton Purdue University, [email protected]Follow this and additional works at: hp://docs.lib.purdue.edu/herrick is document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. Bolton, J Stuart, "e 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. hp://docs.lib.purdue.edu/herrick/82
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Purdue UniversityPurdue e-Pubs
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, [email protected]
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 [email protected] foradditional information.
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
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
27
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.
28
Glass Fiber Material Inside of Glass Fiber Material Inside of Sample HolderSample HolderSample HolderSample Holder
29
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)
30
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
31
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)
32
Variation of Flow ResistivityVariation of Flow Resistivity
40
• Flow resistivity controls TL at low and high frequency limit
30
35
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 )
33
Investigation of Vibrational Investigation of Vibrational Modes of Glass Fiber MaterialsModes of Glass Fiber MaterialsModes of Glass Fiber MaterialsModes of Glass Fiber Materials
34
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)
35
Internal Constraint to Enhance Internal Constraint to Enhance the Sound Transmission Lossthe Sound Transmission Lossthe Sound Transmission Loss the Sound Transmission Loss
36
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]
37
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.
38
Effect of Releasing the Internal Effect 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)
CardboardConstraint
102 1030
5
35
40
(b)
15
20
25
30
TL
(dB) Plexiglass
Constraint
102 1030
5
10
F requenc y (H z)
39
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)
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
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
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
Experimental ValidationExperimental Validationo A good qualitative agreement is observed
between measurements and FE predictions
45
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
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
47
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
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
o Predicted Sound Transmission Loss in Hybrid System with Fibrous Cell Filling
50
• 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
Former Students:• Edward R. Green
• Bryan H. Song
• Jinho Song
• Ryan Schultz
Current Students:y
• Srinivas Varanasi
• Yangfan Liu
52
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/