Micro-perforates in vibro-acoustic systems Li CHENG

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1 Micro-perforates in vibro-acoustic systems Li CHENG Chair Professor and Director Consortium for Sound and Vibration research Department of Mechanical Engineering The Hong Kong Polytechnic University CAV Workshop 2014

2 Overview Introduction of MPP and its conventional applications MPP for interior noise control MPP absorber with irregular-shaped cavities PTF formulation and compound panel treatment Application examples Conclusions

3 What is Micro-perforated Panel (MPP)? MPP were developed by Daa-You Maa (1975) to satisfy the need of incorporating sound absorption material in tough working conditions. Unlike ordinary perforated panels where the perforations are in millimeters or centimeters, the diameters of the holes in MPP were reduced to submillimeter size (diameter mm). Perforated Panel Micro-Perforated Panel High reactance Low resistance Only used as protective facing for porous material Low reactance High resistance Provide sufficient absorption without extra porous material

4 Maa s MPP impedance formula Impedance of a single tube divided by perforation Resistance r = 32m t s c d Z MPP = Z hole sr 0 c = r + jwm é ê ëê 1+ x x d t ù ú ûú σ: porosity r: resistance m: effective mass per unit area d: hole diameter f: frequency t: hole depth c: speed of sound μ: kinematic viscosity of air End correction (sound radiation from the ends of the tube) Reactance m = 32m s c é ê t ê s c 1+ 1 ê ê ë 9 + x d t ù ú ú ú ú û

5 MPP absorber A typical MPP absorber takes the form of a MPP fitted in front of a backing wall. According to Maa s theory, an equivalent circuit method can be used to predict the sound absorption performance (Maa, 1975). MPP Z mpp ρ 0 c CBMPPA Z cavity,θ 2 p i Backing air cavity Absorption coefficient 4r a = (1+ r) 2 + (wm - cot(w D / c)) 2

6 Absorption coefficient Magnitude Helmholtz absorption of MPP absorber The equivalent circuit model is analogous to a lumped parameter system å Mw 0 + Cw 0 + K lx =0,l y w 0 l x =0,l y = F MPP Cavity (-) Cavity (+) Reactance term of the system Peak Dip Frequency (Hz) Absorption curve using Maa s formula

7 Advantages of Maa s model Easy to use Clear working principle Experimental validation through impedance tube test (absorption curve, impedance), or reverberation room test (reverberation time) Flexibility and convenience of accounting for more complex MPP configuration (double or multiple MPPs, flexible MPP, etc) Double MPPs Flexible MPP

8 Absorption coefficient Complex acoustic behavior of MPP absorber An example 1 MPP absorber flush mounted in an infinite baffle Depth mode θ 0.4 Lateral mode θ=0 θ= Lateral modes Depths modes

9 Absorption coefficient Complex acoustic behavior of MPP absorber An example Nature of surrounding acoustic media Backing cavity forms a sound field Lateral modes Depths modes 1k 2k (Yang, Cheng and Pan, JASA 2013)

10 Modeling MPP absorber in compact vibro-acoustic system Boundary integration: 1 p 1 = - jrwò G 1 v 1 ds + ò G 1 QdV Vs p 2 = - jrw s a ò sa G 2 v 2 ds Green s function 2 G(r,r 0 ) = å n j n (r)j n (r 0 ) L n (k 2 - k n 2 ) Boundary conditions 3 v 1 = ( p 1 - p 2 ) / Z mpp v 1 = -v 2 Coupled equations (k 1m 2 - k 2 (1) )L 1m A m + jkc mpp å L m,m' A m' - jkc mpp å R m,n B n = jrckqf m (r s ) m' (k 2 2n - k 2 )L 2n B n + jkc mpp å L (1) n,n' B n' - jkc mpp å R m,n A m = 0 n' m n 4 Domain 1 Domain 2 (1) L m,m' (2) L n,n' R m,n = = ò f m f m' ds Sa a = ò y n y n' ds Sa a f m y n ds a ò Sa Effect of impedance boundary Sound field interaction Backing Domain 2 Domain 1 Q(r s ) MPP Cavity

11 Sound pressure level Locally reactive model vs coupled model (1,0) (2,0) (3,0) (4,0) (5,0) (6,0) (7,0) (8,0) (9,0) Mode (3,0) Performance overestimated! 80 without MPP absorber 60 R S Local reactive model Coupled model Frequency (Hz)

12 Experimental validation MPP with a backing cavity MPP Mic Speaker Experimental setup MPP with a backing cavity

13 Experimental validation MPP with a backing cavity Model validation Effect of MPP backing cavity (Yang and Cheng, 2014) Locally reactive model cannot characterize MPP absorber in complex vibro-acoustic environment The sound field of backing cavity makes considerable influence to the absorption of MPP The involvement of lateral modes usually degrades control performance

14 Abs coeff Further improve absorption performance irregular shaped cavity The sound field of backing cavity has great impact to the absorption performance of MPP absorber, which leaves large space for further improvement through backing cavity design Frequency (Hz) Rectangular Trapezoidal Use geometrical effect to distort the cavity modes Alter the coupling between air mass and cavity modes Enhance the coupling strength at poor absorption region

15 Absorption coefficient Further improve absorption performance irregular shaped cavity Geometry γ= Volume controlled (i.e. zero mode) Dominating cavity mode Frequency Rectangular cav Trapezoidal cav Maa

16 Application of MPP with irregular backing cavity Wave Trapping Barrier Geometrical effect Sound absorption effect Reflecting wall WTB MPP Noise source Willowdale mining site in Western Australia (Pan, Ming and Guo, 2004)

17 Insertion Loss (db) Application of MPP with irregular backing cavity Wave Trapping Barrier Insertion loss comparison (Yang, Pan and Cheng, 2013) 50 No reflecting wall 40 With reflecting wall WTB With reflecting wall Wavelength vs wedge dimension Frequency(Hz)

18 Application of MPP with irregular backing cavity Wave Trapping Barrier Sound pressure distribution 80dB Below 1000Hz Rectangular WTB Rectangular Above 1000Hz WTB 110dB

19 Application of MPP with irregular backing cavity Wave Trapping Barrier Barrier performance comparison of different profiles Poor Medium Best Rectangular(dB) Tilted(dB) WTB(dB) R R Rectangular Barrier (RB) Layout Reflecting wall S1 2m R0 Tilted Barrier (TB) Noise barrier R1 Wave Trapping Barrier (WTB) R7 R8 R9 R4 R5 R6 R2 R3 5m 1m R R R R R R m 10m 20m 50m R

20 Remarks In complex vibro-acoustic system, the acoustic behavior of MPP absorber cannot be characterized in conventional manner The influence of the backing cavity leaves large room for performance optimization

21 Application of MPP in compact systems MRI (Li and Mechefske, 2010) Auto (Cackley and Bolton, 2013) Boat engine (Herrin et al, 2011) Truck engine (Corin and Wester, 2005)

22 Patch Transfer Function (PTF) Formulation Open acoustic medium Cavity S c Open acoustic medium S i Patches 1 - Coupling surfaces divided into elementary surfaces called patches Mechanical Structure (a) Internal partition 2 - PTFs definition for each subsystem: Structural: Y s ij V F s i s j Acoustical: Z a ij F V a i a j Calculation: FEM, BEM, analytical, (b) 3 Assembling using continuity relations and superposition principle PTF substructuring

23 PTF of MPP Equation of motion for a hole: Re 0 s Z u u i Im Z u p p where 0 u 1 u u u 1 s 0 1 Z 0 u s p 1 0 p 2 c is the complex acoustic impedance of the hole Mean velocity of the surrounding air particle (homogeneization): 0 Suppressing the air velocity in the hole u, with 1 Re Z Z 0cZ (MPP transmissibility) (equivalent mobility of the perforation) s MPP equivalent mobility: Y = Y + eqij p ij Description of pressure and velocity variables for the MPP

24 Coupling treatment Superposition principle for linear passive systems: N s s s s ui ui Yij f j j 1 N i i ij j j 1 f f Z u, 1,2 1 Patch velocities obtained by introducing these relations in the continuity conditions in the presence of a micro-perforated structure: u I Ψ 1 Y s Z Z u s Ψ 1 Y s f f Resulting pressure inside the fluid domain: p M N ~ pm ZiM i 1 u 1 i

25 MPP in Complex Environment Rigid duct Partial plate Micro-perforations 1. Typical applications: ventilation window, duct silencer, partition inside enclosure, etc 2. Mixed separation interface: rigid or flexible structure, air aperture, MPP Rigid Structure Domain I n D2 Flexible Structure n D1 Aperture Domain II 3. Parallel structural and acoustic sound transmission paths between acoustic media

26 Compound Panel Subsystem Aperture with thin thickness assumption: - Taylor series expansion: pa pa( x, y, z) pa( x, y, z0) ( z z0) z - Cross-thickness velocity: Virtual panel treatment of an air aperture V z n 1 p ( x, y, z ) a (1 ˆ ) n a j z c a 0 a 0 n 0 z - Aperture mobility: a V i j 1 aij ( ) a 2 2 a i a j F j 0Lz s n N a S S Y ds ds i j Virtual Panel p V i j 1 - Panel mobility: Y p ds ds F php( m ) s m N p pij p i p j j s s i j

27 Compound Panel Subsystem Y 0 0 F a V a a 0 Yp Yp-mpp Fp Vp 0 F mpp V Ympp- p Ympp mpp Mobility matrix Excitation Response A compound panel surrounded by two acoustic media Description of a compound panel Combine rigid/flexible structure, aperture, MPP into a single structural interface

28 Compound Panel Subsystem Thickness Criterion Rectangular cavity with enclosed partial structure Validation against FEM Effective thickness criterion test: Percentage error between the proposed approach and exact value: PE ( P P ) / P vp bt bt Criterion of s /4 provides satisfactory accuracy Criterion of s /16 fully guarantees the accuracy

29 Various Applications Rigid/flexible and micro-perforated partition: 128Hz 128Hz 1. MPP brings a noticeable pressure balance across the partition 2. MPP adds system damping by means of energy dissipation through the holes 63Hz

30 Various Applications Radiation from a partially covered enclosure Semi-infinite acoustic domain Partial flexible plate Receiving point Rigid baffle Rigid baffle Point source Acoustic enclosure z y x 1. The interface being treated as compound panel can be any combination of structure and aperture 2. Sound scattering pattern can be clearly observed

31 Various Applications Effect of adding MPP absorbers: Internal MPP absorbers improve TL Absorption behavior is very complicated Require fully-coupled modeling tools

32 Various Applications Interior and Exterior domains are infinite duct 0.36m Exterior domain Interior domain 0.84m Double-glazed ventilation window system Validation of the model against FEM

33 Various Applications Baffle MPP Solid Empty MPP Baffle 0.3m Effect of additional MPPs Solid MPP

34 Application to Duct Silencer Empty expansion chamber Reactive expansion chamber silencer 1. The proposed approach is more computational efficient than FEM 2. Numerical studies provide silencer design guidance Complex internal partitions

35 Application to Duct Silencer Complex silencer configuration with rigid/mpp internal partitions Hybrid silencers Effect of MPP

36 Application to Duct Silencer Experimental measurement: Vibration of internal partitions attributed to thin structures may deteriorate the silencing effect performance overestimated!

37 Remarks A sub-structuring approach to model complex vibro-acoustic systems involving cascade structures coupled with partially opened/closed acoustic cavities is developed. The proposed compound panel treatment allows a systematic handling of the mixed separations/interfaces comprising any combination of rigid/flexible structure, aperture and MPP, and converts the parallel sound transmission between acoustic media into a serial one. The proposed approach provides an efficient and versatile simulation tool to predicate the effect of multiple rigid/flexible partial partitions and micro-perforated elements inside complex acoustic systems, such as duct silencers or ventilation windows. Benefiting from the substructuring nature, numerical calculation and optimization is less time consuming compared with existing modeling techniques.

38 Concluding Remarks Micro-perforates provide a non-fibrous, environmental-friendly and effective sound absorption materials with great potential. Design, tuning and optimization are possible by making use of vibroacoustic principles Acoustic behavior of the MPP strongly depends on the vibroacoutic working environment. MPP should be regarded as an integrative part of the system Flexible tools, capable of dandling system complexities and conducive to system optimizations, are needed.

39 Micro-perforates in vibro-acoustic systems Li CHENG Chair Professor and Head Department of Mechanical Engineering The Hong Kong Polytechnic University Xiang Yu Cheng Yang Jean-Louis Guyader J. Pan Laurent Maxit