Porous Materials for Sound Absorption and Transmission Control

Transcription

1 Purdue e-pubs Publications of the Ray W. School of Mechanical Engineering Porous Materials for Sound Absorption and Transmission Control J Stuart Bolton, bolton@purdue.edu Follow this and additional works at: Bolton, J Stuart, "Porous Materials for Sound Absorption and Transmission Control" (2005). Publications of the Ray W. Herrick Laboratories. Paper This document has been made available through Purdue e-pubs, a service of the Libraries. Please contact epubs@purdue.edu for additional information.

2 Porous Materials for Sound Absorption and Transmission Control J. Stuart Bolton Ray W. it

3 Introduction What are Porous Media? Two phases Solid Fluid What do they do? Convert organized acoustical motion into heat What don t they do? Dissipation of Energy Block sound : i.e., not usually useful as barriers (by themselves)

4 Introduction Dissipation mechanisms Viscous Thermal Structural Examples of porous materials Glass fiber Mineral wool Open or partially open cell foams Applications Automotive, Aircraft,

5 SEM Glass Fiber

6 SEM Resinated Glass Fiber

7 SEM Partially Reticulated Foam

8 SEM Shoddy

9 SEM Thinsulate

10 Sound Propagation in Porous Porous Materials Media Two phases: Solid (frame) and gas (air) Allow two longitudinal wave types which appear in both phases Allow transverse wave motion if frame possesses shear stiffness Display large sensitivity to boundary conditions if frame is relatively stiff (modulus near that of air)

11 Transmission Measurements Test signal: Linear Frequency Sweep, 0 Hz-25 khz, 20 ms Sample Rate: 100 khz Resolution: 12 bits Post-Acquisition: Resample to 50 khz

12 Foam Impulse Response Note: Frame Wave- first arrival

13 Absorption treatments Bonded/Bonded membrane foam backing Bonded/Unbonded airspace Unbonded/Bonded Unbonded/Unbonded

14 Normal Incidence Absorption Effects of Airspace at front and rear 1. Film/Foam/Backing 2. Film/Space/Foam/Backing 3. Film/Foam/Space/Backing /S /B 4. Film/Space/Foam/Space/Backing Foam 25 mm, 30kg/m 3 Membrane kg/m 2 Airspaces 1 mm

15 Characterization ti of Porous Media Rigid Solid phase does not move Frame bulk modulus significantly greater than that of air Airborne wave only *situations in which frame is not excited directly Porous ceramics Sintered metals

16 Characterization ti of Porous Media Limp Solid phase moves driven by fluid motion only Frame bulk modulus significantly less than of air Airborne wave only Limp glass fibers, thinsulate and other fibrous media

17 Characterization ti of Porous Media Elastic Solid phase moves Frame bulk modulus of same order of that as air Airborne, frame and shear waves Boundary d conditions are very important t Polyurethane and polyimide foams

18 Elastic Physical Properties of Porous Media Acoustical properties are determined by macroscopic physical properties. p Limp gid Ri - Flow resistivity - porosity Fluid-acoustical parameters - pore tortuosity - Bulk density - In vacuo bulk modulus - Shear modulus - Loss factor Elastic properties With knowledge of these properties the acoustical performance of porous media can be predicted.

19 Physical Properties of Porous Media Flow Resistivity Resistance to steady state flow through a porous material Determined by - pore tortuosity - viscous drag When pores are straight, measure of viscous dissipation potential

20 Measurement of Physical Properties- Flow Resistivity

21 Physical Properties of Porous Media Tortuosity Measure of deviation of pore from straight line through h material Ratio of actual path length through material to linear path length Results in inertial coupling between solid and fluids phases Ranges from 1 (low density fibrous material) to 10 (partially reticulated foam)

22 Modeling of Porous Media Objective Limited Material Microstructure Well Developed Analytical Well Developed Macroscopic Properties Fundamental Acoustic Properties Installed Acoustic Properties Numerical Initial Work

23 Microstructure to Macrostructure For fibrous media made up of mono-diameter fibers (e.g., from Beranek, Noise and Vibration Control)

24 Modeling of Porous Media Approach followed by Bolton and Allard Based on theory of elastic porous materials by Biot (1956): - Allows transverse wave motion - Expressed in very general form - Most widely used in geophysics Here: - Adapt theory to acoustic porous materials (i.e., foam and glass fiber) - Express in terms of conventional variables (i.e., displacement and pressures) - Derive boundary conditions applicable to typical reflection and transmission problems Results: - First theory capable of predicting oblique incidence behavior of foam in noise control application

25 Theoretical Approach WRITE: - stress-strain strain relations for each phase - Dynamic relations for each phase COMBINE TO YIELD TWO WAVE EQUATIONS: - Volumetric strain - Rotational strain FROM SOLUTIONS DERIVE: - Displacement fields - Normal and shear stresses at boundaries DETERMINE COMPONENT AMPLITUDES: - By application of boundary conditions

26 Notation Forces acting on solid phase/unit material area: Forces acting on fluid phase/unit material area: * Notes: 1. s = - hp, where h=porosity 2. Solid displacement denoted by ū 3. Fluid displacement denoted by Ū

27 The RAYLEIGH Model The original model The modified model (allowing for pore tortuosity) t

28 Fluid-Structural Coupling Inertial proportional to relative acceleration Viscous proportional to relative velocity

29 Dynamic Relations ) ( ) ( 1) ( y y y y y xy y U u t b U u t q t u x y Solid: y y y y t t t x y ) ( ) ( 1) ( y u U b u U q U s Fluid: ) ( ) ( 1) 2 ( y y y y u U t b u U t q t y where = bulk density of frame where ρ 1 = bulk density of frame ρ 2 =ρ 0 h (bulk fluid density) q 2 = structure factor (inertial coupling) q structure factor (inertial coupling) b = viscous coupling factor * Note : Viscous and inertial coupling

30 Wave Equations 4 2 Volumetric Strains: e A e Be 0 Solution of form: jk 1, 2 Ce x Where: k 2 1,2 A A 2 2 4B Note: two longitudinal wave types distinguished by different wave numbers: i.e., Airborne wave Frame wave

31 Wave Equations 2 2 Rotational Strains: z k 0 t z Solution of form: Ce jk t x Where: ω z = z-component of k t = transverse wave wave number Note: single transverse wave type

32 Phase Speed and Attenuation Phase Speed Attenuation

33 Forms of Solutions e [ C 1 e jk 1 y y C 2 e jk 1 y y C 3 e jk 2 y y C 4 e jk 2 y y ] e jk x x z jk ty y [ C 5 e C 6 ty C e ] jk y e jk x x where: k k k 2 2 1, 2 y 1, 2 y x and k ty k 2 t k 2 x Then derive:, and z, u, u, u, u, U, U, U, U l x t x, s, y l xy y t x l x t x l y t x

34 Solid Displacement: u y je jk Forms of Solutions x x k 1 y jk k 1 y y 1 y e C k 1 k 1 k k jk 1 1 y 2 y jk k 2 y y 2 y e C k 2 e jk 2 2 y k e y C y 2 C 4 Longitudinal k x jk x jk y jk y e C e C e x ty j k t ty Transverse Similar expression for U y,σσ y,ττ xy, etc., all in terms of six unknown constants C 1 -C 6 ; they are determined by application of the boundary conditions.

35 Sound Transmission Through Double Panels Approach: Substitute allowed solutions into boundary conditions. Arrange as matrix problem in wave amplitudes and solve for required coefficients.

36 Open Surface: Boundary Conditions 1. Volume Velocity: v y = iω [ (1-h) u y + h U y ] 2. Fluid Force: -h p = s 3. Solid Force: - (1-h) p = σ y 4. Shear Force: τ xy = 0

37 Boundary Conditions Bounded Euler-Bernoulli Plate (D, m s ): 1. Normal Velocity: v y = iω W 2. Solid Displacement: u y = W 3. Fluid Displacement: U y = W 4. Tangential Displacement: u x = - (h 1 /2) W/ x Eqn. of Motion: W W h D m s ( y s ) p 4 2 x t 2 ( 1 xy x Note: 1. transverse wave excitation through plate thickness affects coupling.

38 Absorption treatments Bonded/Bonded membrane foam backing Bonded/Unbonded airspace Unbonded/Bonded Unbonded/Unbonded

39 Normal Incidence Absorption Effects of Airspace at front and rear 1. Film/Foam/Backing 2. Film/Space/Foam/Backing 3. Film/Foam/Space/Backing /S /B 4. Film/Space/Foam/Space/Backing Foam 25 mm, 30kg/m 3 Membrane kg/m 2 Airspaces 1 mm

40 Sound Absorption Treatments Owing to high impedance frame waves 1. Loose surface membrane yields better overall sound absorption than bonded membrane (with exception of very low frequencies). 2. Small airspace (~ 1 mm) behind foam layer enhances low frequency performance with or without front membrane. 3. Light, loose membrane on foam with thin backing space gives performance as good as unfaced foam while protecting foam.

41 Sound Transmission Through Approach: Double Panels Substitute allowed solutions into boundary conditions. Arrange as matrix problem in wave amplitudes and solve for required coefficients

42 Transmission Loss Measurements Procedure - Measure 1/3 octave mean square pressure in source room ( Ii ) - Measure 1/3 octave transmitted intensity averaged over panel area ( It ) - TL = 10 log ( Ii / It )

43 Test Panel Mounting

44 Foam Mounting Note: Panel Dimensions 1.2 m by 1.2 m

45 Panel Configurations Tested Foam: 30 kg/m 3 26 mm thick Panel: Aluminum 0.05 and 0.03 thick Panel Separation: 26 mm to 41 mm

46 Transmission Loss Double Panel: Lined & 0.03 Theory Experiment Foam UNBONDED to incident side panel

47 Transmission Loss Double Panel: Lined & 0.05 Theory Experiment Foam BONDED to both panels

48 Transmission Loss Double Panel: Lined & 0.05

49 Sound Transmission High impedance frame wave causes performance to depend on mounting. Avoid direct excitation of frame waves - do not continuously bond foam to backing - do not continuously bond surface treatments to foam Bonded attachment - Shifts mass-air-mass resonance to higher frequencies - Decreases high frequency transmission loss

50 Multi-layer models and GUI program Develop various combinations of iso. or aniso. foam, stiff panel and air layers. Implement user-friendly program running as GUI form. Organizing i by GUI

51 Aircraft Application Conventional ribbed-aluminum fuselage Y X Honeycomb core Different stiffness in X,Y & Z dir. solid and fluid (air) parts Replaced by Nomex honeycomb sandwich Panel Z Z Y Transversely poro-elastic modeling X Transversely isotropic properties 5 elastic constants : E x = E y, E z,g zx,v xy,v zx Porous foam with constants, porosity, bulk density, flow resistivity and tortuosity

52 TL for 1/2 lined and unlined Fuselage Example Lined model 80 Lined with 1/2 glass fiber prediction measurement Unlined model Unlined - 1/2 air layer TL (db) prediction 20 measurement 10 * About 15dB improvement above 1kHz by lining with ½ fibrous material in the air space between honeycomb panel and the interior trim Frequency (Hz)

53 Finite Element Modeling Practical Treatments

54 Shape Optimization of Foam Wedge Objective maximize absorption offered by a wedge over a specified frequency range rigid piston constrained edges air f oam u o e jt a y x hard wall L c d - Wedge defined by θ when volume and a is held constant - Given volume find optimum angle, θ

55 Shape Optimization of Foam Wedge (a) (b) = 36o (optimal wedge) = 132 o 0.2 = 180 o Frequency (Hz) wedge tip angle ()

56 System Configurations - In system (b), tortuosity of a foam layer is varied spatially across the duct (in y-direction).

57 Sound Transmission Through A Wedge

58 Sound Transmission Through A Foam Layer Having Spatially Graded Tortuosity

59 Experimental Setup High Frequency Tube B & K Type 3560 Pulse System (Four Channel) Signal Generator Signal Amplifier Kg m 2.9 cm 7.5 cm Microphones Aviation grade glass fiber Anechoic Termination New Sample Holder Two-Microphone Impedance Measurement Tube B&KType4206

60 Anechoic Transmission Loss Experiment Prediction using FEM (with edge constraint) Prediction without edge constraint 30 TL (db) Increase in TL due to edge 5 constraint Shearing mode Frequency (Hz)

61 Constrained around Edge (50 Hz Hz) Experiment FEM TL (db) Hz 280 Hz Frequency (Hz)

62 Laser Measurement Setup (Large Tube, 1 Sample A) x B & K Type 3560 Pulse System (Four Channel) Computer A B d x 2 x 1 Polytec Fiber OFV 3000 Controller Signal Generator Signal Amplifier Polytec Fiber OFV 511 Fiber interferometer Sample Plexiglass Two-Microphone Impedance Measurement Tube B & K Type 4206

63 The 1 st and 2 nd Mode Shapes of the Edge-constrained Sample (1 ) FEM (a) Experiment (b) st Mode at 100 Hz vf/p / vf/p ma ax vf/p / vf/p ma ax y y x x (c) (d) nd Mode at 350 Hz vf/p / vf/p max vf/p / vf/p max y y x x

64 Summary Three types of porous media: rigid, limp and elastic Wave propagation can be modeled d accurately using Biot theory and later variants Given values for macroscopic parameters, acoustical behavior of sound absorbing materials can be accurately predicted Foam finite elements can be used to model arbitrarilyshaped treatments

65 Future Challenges Anisotropy all noise control materials are anisotropic Inhomogeneity all noise control materials are inhomogeneous Nonlinearity all noise control materials are nonlinear Inhomogeneous treatments spatially distributed properties to improve dissipation Material optimization especially foams and fibrous materials Addition of tuned elements to fibers SEA compatible models