The Influence of Boundary Conditions and Constraints on the Performance of Noise Control Treatments: Foams to Metamaterials

Transcription

1 Purdue University Purdue e-pubs Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering 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: 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 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.

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 supports Metamaterial Barrier 2

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5 Normal Incidence Measurement of Reflection 4

6 Film-faced 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 membranes 5

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

8 One-Dimensional Poroelastic Material Theory Equations of motion: Fluid: Solid: Based on Zwikker and Kosten, plus Rosin with complex density and air stiffness taken from Attenborough. 7

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

10 Reflection Impulse Response - Predicted Open Surface Foam Film-faced Foam Reflection from rear surface Disaster! 9

11 Film-faced Foam / Thin Air Gap Impedance: 10

12 Film-forced Foam / Thin Air Gap Inverted reflection from rear surface 350 Hz 1600 Hz 11

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

14 o Bonded/Bonded membrane foam backing o Bonded/Unbonded airspace o Unbonded/Bonded o Unbonded/Unbonded 13

15 Normal Incidence Absorption o Foam 25 mm, 30kg/m 3 o Membrane kg/m 2 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 4. Film/Space/Foam/Space/Backing 14

16 Impedance Tube Testing Melamine Foam (8.6 kg/m 3 ) 100 mm diameter 25 mm thick Each sample fit exactly by trimming the diameter & checking the fit with a TL measurement Two Facing & Two Rear Surface Boundary Conditions Multiple trials Multiple samples 15

17 Sample Fit: TL Qualification Transmission Loss Non-Zero TL = Sample Constrained As-Cut 1 st Trim 2 nd Trim 3 rd Trim Zero TL = Sample Free to Move 4 th Trim No Leakage 16

18 Surface Configurations Front Surface: Rear Surface: Loose Glued 1) Plastic film near, but not adhered to foam 2) Plastic film glued to foam Gap Fixed 1) Small gap between foam & rigid wall 2) Foam adhered to rigid wall 17

19 Absorption vs. Configuration - Test Absorption Coefficient Loose - Gap Loose - Fixed Glued - Gap Glued-Fixed 18

20 Helmholtz Resonator Effect? Mechanical Impedance Mass Stiffness Total Acoustic Impedance 19

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

22 Helmholtz Resonator Effect? But is it really due to edge gaps? Measured Glued Facing + Fixed with Edge Sealed 21

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24 Resting on Floor Bonded to Backing 23

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26 Tensioned Membranes Model Verification Velocity Measurement 25

27 y y v/p / v/p max v/p / v/p max Model Verification Vibrational Modes Theory Experiment Absolute velocity of membrane - Experiment st y x y Magnitude nd x

28 Model Verification Experiment Set-up 27

29 Model Verification Model Optimization o Given experimental results as input, Find appropriate material properties (T o, ρ s, η ) Why this behavior? Finite size, held at edge, finite stiffness. 28

30 Glass Fiber Material Inside of Sample Holder 29

31 TL (db) Anechoic Transmission Loss (Green) Experiment FE Prediction (Edge constrained) Prediction (Unconstrained case) Increase in TL due to edge constraint (10dB) Shearing mode Frequency (Hz) 30

32 Poroelastic Material Properties Used in Calculations Material Bulk density (Kg/m 3 ) Porosity Tortuosity Estimated flow resistivity (MKS Rayls/m) Shear modulus (Pa) Loss factor Yellow Green

33 TL (db) Variation of Shear Modulus o As shear modulus increases, the minimum location of TL moves to higher frequencies Shear Modulus = 1000 Pa Shear Modulus = 2000 Pa Shear Modulus = 3000 Pa Shear Modulus = 4000 Pa Frequency (Hz) 32

34 TL (db) Variation of Flow Resistivity Flow resistivity controls TL at low and high frequency limit Flow resistivity = MKS Rayls/m Flow resistivity = MKS Rayls/m Flow resistivity = MKS Rayls/m Flow resistivity = MKS Rayls/m Frequency (Hz) 33

35 Investigation of Vibrational Modes of Glass Fiber Materials 34

36 vf/p / vf/p max vf/p / vf/p max vf/p / vf/p max vf/p / vf/p max Vibrational Modes of Fiber Glass Materials (1st and 2nd Modes, Green) FEM Experiment st (133 Hz) y x 0 (a) y x 0 (b) nd (422 Hz) y x 0 (c) y x 0 (d)

37 Internal Constraint to Enhance the Sound Transmission Loss 36

38 Sound Transmission Loss (Experiment, Green) [Density of Plexiglass: 1717 Kg/m3] 37

39 TL (db) TL(dB) Effect of Releasing the Internal Cross- Constraint (Measurement) With constraint Without constraint (a) Cardboard Constraint (b) Plexiglass Constraint Frequency (Hz) Relatively heavy constraint required to realize low frequency benefit. 38

40 TL (db) TL (db) Effect of Releasing the Internal Cross- Constraint (FEM Prediction) With constraint Without constraint (a) Cardboard Constraint (b) Plexiglass Constraint Frequency (Hz) 39

41 Metamaterials 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. From : Meta-Material Sound Insulation by E. Wester, X. Bremaud and B. Smith, Building Acoustics, 16 (2009) 40

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43 Proposed Mass-Neutral Material Homogenized mat. Cellular panel nl Frame (Mat. A) Meff : Meff f 2 0c T 2 c j2 fm 0 eff STL 20log T Meff : Mass per unit area STL : Sound Transmission Loss f nl L L Plate (Mat. B) Unit cell 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 of a unit cell for normally incident sound 42

44 Low 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 Material-Based Mass Apportioning Each unit cell Overall mass constant Different materials for frame and plate A series of cases for μ between 0.1 and ρ p and ρ f varied E f varied keeping E p constant so that Ef Ep f p Mat. A Mat. B Base unit cell Cellular unit cell 44

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

47 Material-Based Mass Apportioning As µ High STL region broadens in the low frequency regime Region between the first peak and dip is widening The dip being shifted to the right desirable µ O(100) saturates E p = 2 GPa 46

48 Effective Mass as a Function of Frequency Magnitude of M eff higher than space-averaged areal mass in the range of Hz An order of magnitude higher in Hz range Shows strong negative mass effect in the peak STL region T 2 0c c j fm f eff 47

49 Mechanism Behind High STL o o o Averaged displacement phase switches from negative to positive value at the STL peak Parts of the structure move in opposite directions similar to observations in LRSMs resulting in zero averaged displacement Negative mass observed without locally resonant elements 48

50 Hybrid Material o o Cellular structure increases STL at low frequencies Lightweight, fine fiber fibrous layer can be used to recover performance at higher frequencies 49

51 Hybrid Material Low Sound Speed Front Metamaterial Core Fibrous Cell Filling Directs non-normally incident sound to core Locally resonant core Fibrous cell filling 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 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 would require supplementary material to mitigate performance loss at high frequencies 51

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

54 pp. 3 11: J. Stuart Bolton, Ph.D. Thesis, University of Southampton, Cepstral techniques in the measurement of acoustic reflection coefficients, with applications to the determination of acoustic properties of elastic porous materials. pp : J. Stuart Bolton, Paper DD4 presented at 110th meeting of the Acoustical Society of America, Nashville TN, November 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 : Ryan Schultz and J. Stuart Bolton, Proceedings of INTER-NOISE 2012, New York City, August, Effect of solid phase properties on the acoustic performance of poroelastic materials. pp : Jinho Song and J. Stuart Bolton, Proceedings of INTER-NOISE 2002, paper N574, 6 pages, Dearborn, Michigan, August Modeling of membrane sound absorbers. pp : Bryan H. Song, J. Stuart Bolton and Yeon June Kang, Journal of the Acoustical Society of America, Vol. 110, , Effect of circumferential edge constraint on the acoustical properties of glass fiber materials. pp : Bryan H. Song, and J. Stuart Bolton, Journal of the Acoustical Society of America, Vol. 113, , Investigation of the vibrational modes of edge-constrained fibrous samples placed in a standing wave tube. pp : Bryan H. Song and J. Stuart Bolton, Noise Control Engineering Journal, Vol. 51, 16-35, Enhancement of the barrier performance of porous linings by using internal constraints. pp : Srinivas Varanasi, J. Stuart Bolton, Thomas Siegmund and Raymond J. Cipra, Applied Acoustics, Vol. 74, , 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 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. 53