Projeto Tratamentos Isolantes Acusticos (11)98950-3543

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Projeto Tratamentos Isolantes Acusticos (11)98950-3543

  1. 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. 2. J. Stuart Bolton Ray. W. Herrick Laboratories School of Mechanical Engineering Purdue University RASD 2013, Pisa, Italy, July, 2013
  3. 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. 4. 3
  5. 5. Normal Incidence MeasurementNormal Incidence Measurement f flf flof Reflectionof Reflection 4
  6. 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. 7. Reflection Impulse ResponseReflection Impulse Response (Film-faced surface up) (Foam-open surface up) 6
  8. 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. 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. 10. Reflection Impulse ResponseReflection Impulse Response --p pp p PredictedPredicted Film-faced FoamOpen Surface Foam Reflection from  rear surface Disaster! 9
  11. 11. FilmFilm--faced Foam / Thin Air Gapfaced Foam / Thin Air Gap/ p/ p Impedance: 10
  12. 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. 13. Rear Surface Boundary ConditionsRear Surface Boundary Conditions 25mm foam layer with bonded membrane 1. No Airspace: 2. Airspace:p 12
  14. 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. 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. 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. 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. 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. 19. Absorption vs. ConfigurationAbsorption vs. Configuration -- TestTest Absorption Coefficient Loose - Gap -- TestTest Loose - Fixed Gl d GGlued - Gap Glued-Fixed 18
  20. 20. Helmholtz Resonator EffectHelmholtz Resonator Effect ?? M h i l I dMechanical Impedance Mass StiffStiffness Total Acoustic Impedance 19
  21. 21. Helmholtz Resonator EffectHelmholtz Resonator Effect ?? Combined Foam + Helmholtz Resonator System is Similar to Measured System 20
  22. 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. 23. 22
  24. 24. Resting on Floor Bonded to Backing 23
  25. 25. TensionedTensioned MembranesMembranes ModelModel VerificationVerification –– Velocity MeasurementVelocity MeasurementModelModel VerificationVerification –– Velocity MeasurementVelocity Measurement 25
  26. 26. 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
  27. 27. Model VerificationModel Verification –– ExperimentExperiment SetSet--upupSetSet--upup 27
  28. 28. 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
  29. 29. Glass Fiber Material Inside ofGlass Fiber Material Inside of Sample HolderSample HolderSample HolderSample Holder 29
  30. 30. 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
  31. 31. 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
  32. 32. 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
  33. 33. 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
  34. 34. Investigation of VibrationalInvestigation of Vibrational Modes of Glass Fiber MaterialsModes of Glass Fiber MaterialsModes of Glass Fiber MaterialsModes of Glass Fiber Materials 34
  35. 35. 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
  36. 36. Internal Constraint to EnhanceInternal Constraint to Enhance the Sound Transmission Lossthe Sound Transmission Lossthe Sound Transmission Lossthe Sound Transmission Loss 36
  37. 37. 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
  38. 38. 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
  39. 39. 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
  40. 40. 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
  41. 41. 41
  42. 42. 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
  43. 43. 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
  44. 44. 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
  45. 45. Experimental ValidationExperimental Validation o A good qualitative agreement is observed  between measurements and FE predictions 45
  46. 46. 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
  47. 47. 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
  48. 48. 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
  49. 49. 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
  50. 50. 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
  51. 51. • 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
  52. 52.  Former Students: • Edward R. Green • Bryan H. Song • Jinho Song • Ryan Schultz  Current Students: y • Srinivas Varanasi • Yangfan Liu 52
  53. 53. 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

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