micro-perforates in vibro-acoustic systemsmicro-perforates in vibro-acoustic systems li cheng chair...

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

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

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 0.1-1 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

End correction (sound radiation from the ends of the tube)

Maa’s MPP impedance formula

Impedance of a single tube divided by perforation

ZMPP

=Z

hole

sr0c

= r + jwm

r =32m

s c

t

d1+

x2

32+

2

8x

d

t

é

ë

êê

ù

û

úú

m =32m

s c

t

s c1+

1

9 +x2

2

+ 0.85d

t

é

ë

êêêê

ù

û

úúúú

Resistance

Reactance

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

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

Backing air cavity

2 pi

ρ0c

Zmpp

Zcavity,θCBMPPA

Absorption coefficient

a =4r

(1+ r)2 + (wm- cot(w D / c))2

Helmholtz absorption of MPP absorber

0 200 400 600 800 1000 1200 1400 1600 1800 2000 0

0.2

0.4

0.6

0.8

1

Peak

Dip

Frequency (Hz)

Ab

sorp

tio

n

coef

fici

ent

100

102

104

106

108

MPP Cavity (-) Cavity (+)

Ma

gn

itu

de

Absorption curve using Maa’s formula

Mw0+ Cw

0+ K

lx=0,l

y

w0

lx=0,l

y

å = F

The equivalent circuit model is analogous to a lumped parameter system

Reactance term of the system

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

Complex acoustic behavior of MPP absorber – An example

θ

0 400 800 1200 1600 2000 0

0.2

0.4

0.6

0.8

1

θ=0 °

θ=45 °

Ab

sorp

tio

n c

oef

fici

ent

Depth mode

Lateral mode

MPP absorber flush mounted

in an infinite baffle

Lateral modes

Depths modes

Complex acoustic behavior of MPP absorber – An example

0

40

80

0

1k

2k

1

2

Abso

rpti

on c

oef

fici

ent

Lateral modes

Depths modes

Nature of surrounding acoustic media Backing cavity forms a sound field

(Yang, Cheng and Pan, JASA 2013)

Modeling MPP absorber in compact vibro-acoustic system

Domain 1

Domain 2

Q(rs)

Backing

MPP

Cavity

p

2= - jrw G

2v

2ds

sa

ò p

1= - jrw G

1v

1ds

sa

ò + G1QdV

Vs

ò

Boundary integration: 1

v

1= ( p

1- p

2) / Z

mpp

Boundary conditions 3

G(r,r0) =

jn(r)j

n(r

0)

Ln(k 2 - k

n

2 )n

å

Green’s function 2

v

1= -v

2

(k1m

2 - k 2 )L1m

Am

+ jkCmpp

Lm,m'

(1) Am'

m '

å - jkCmpp

Rm,n

Bn

n

å = jrckqfm(r

s)

(k2n

2 - k 2 )L2n

Bn+ jkC

mppL

n,n '

(1) Bn '

n '

å - jkCmpp

Rm,n

Am

m

å = 0

4

Lm,m '

(1) = fmf

m 'dS

aSa

ò

Ln,n '

(2) = yny

n 'dS

aSa

ò

Rm,n

= fmy

ndS

aSa

ò

Coupled equations

Effect of impedance boundary

Sound field interaction

Domain 1

Domain 2

Locally reactive model vs coupled model

0 200 400 600 800 1000 1200 1400 1600 1800 2000 40

60

80

100

120

140

160

180

without MPP absorber

Coupled model S

R

So

un

d p

ress

ure

lev

el

Frequency (Hz)

(1,0) (2,0) (3,0) (4,0)

(5,0) (6,0) (7,0) (8,0)

(9,0)

Local reactive model

Mode (3,0)

Performance overestimated!

Experimental validation – MPP with a backing cavity

Experimental setup

MPP with a backing cavity

MPP

Speaker

Mic

Experimental validation – MPP with a backing cavity Model validation Effect of MPP backing cavity

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

(Yang and Cheng, 2014)

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

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

0 400 800 1200 1600 2000 0

0.2

0.4

0.6

0.8

1

Frequency (Hz)

Ab

s co

eff

Further improve absorption performance – irregular shaped cavity

Volume

controlled (i.e.

zero mode)

Dominating cavity mode

0 500 1000 1500 2000 2500 3000 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Ab

sorp

tio

n c

oef

fici

ent

Frequency

Rectangular cav

Trapezoidal cav

Maa

γ=10°

Geometry

Application of MPP with irregular backing cavity – Wave Trapping Barrier

Reflecting wall

WTB

Noise source

MPP

Geometrical effect Sound absorption effect

Willowdale mining site in Western Australia (Pan,

Ming and Guo, 2004)


Wavelength vs wedge dimension

0 500 1000 1500 2000 2500 3000 3500 4000 -30

-20

-10

0

10

20

30

40

50

With reflecting wall

No reflecting wall

Inse

rtio

n L

oss

(d

B)

Frequency(Hz)

WTB With reflecting wall

Insertion loss comparison (Yang, Pan and Cheng, 2013)


Below 1000Hz Above 1000Hz Rectangular WTB Rectangular WTB

Sound pressure distribution 110dB 80dB


Rectangular

Barrier (RB)

Tilted Barrier

(TB)

Wave Trapping Barrier

(WTB)

1 1 1

0.02

60°

10°

0.02 0.02

10m

2m

R1 S1

R0

0.9m

R2 R3

R4 R5 R6

R7 R8 R9

1m

5m

20m

50m

Reflecting

wall Noise

barrier

Barrier performance comparison of different profiles

Layout

Rectangular(dB) Tilted(dB) WTB(dB)

R1 7.2 11.8 13.2

R2 6.2 11.3 12.4

R3 5.5 10.9 11.9

R4 10.7 16.0 17.3

R5 10.1 15.2 16.8

R6 10.5 15.9 17.1

R7 3.2 2.0 3.8

R8 4.5 7.4 10.6

R9 7.8 13.7 14.7

Poor Medium Best

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

Application of MPP in compact systems

MRI (Li and Mechefske, 2010)

Boat engine (Herrin et al, 2011) Truck engine (Corin and Wester, 2005)

Auto (Cackley and Bolton, 2013)

iS

Patches

Mechanical

Structure

Cavity

Internal

partition

Sc

Open acoustic

medium

Open acoustic

medium

(a)

(b)

PTF substructuring

2 - PTFs definition for each subsystem:

1 - Coupling surfaces divided into

elementary surfaces called “patches”

Calculation: FEM, BEM, analytical,…

3 – Assembling using continuity relations and superposition principle

s

is

ij s

j

VY

F

Z

a

ia

ij a

j

F

V

Structural:

Acoustical:

Patch Transfer Function (PTF) Formulation

21

00

0

0

0

0

1ImRe pp

cuZiuuZ s

1 01 su u u

211 ppuu s

0 01 Re Z Z

0 0 0c Z

Description of pressure and velocity variables for the MPP

Equation of motion for a hole:

0Zwhere is the complex acoustic impedance of the hole

Mean velocity of the surrounding air particle (homogeneization):

with (MPP transmissibility)

(equivalent mobility of the perforation)

Suppressing the air velocity in the hole , 0 u

PTF of MPP

MPP equivalent mobility: = +s

eqij p ijY Y

1

Ns s s s

i i ij j

j

u u Y f

1

, 1,2N

i i ij j

j

f f Z u

1

1 1 2 1 2u I Ψ 1 Y Z Z u Ψ 1 Y f fs s s

Superposition principle for linear passive systems:

Patch velocities obtained by introducing these relations in the continuity

conditions in the presence of a micro-perforated structure:

N

i

iiMMM uZpp1

1~

Resulting pressure inside the fluid domain:

Coupling treatment

MPP in Complex Environment

Partial plate

Micro-perforations

Rigid duct

1. Typical applications: ventilation

window, duct silencer, partition

inside enclosure, etc…

Domain I

Domain II

Flexible Structure

Aperture

Rigid Structure

1nD

2nD

2. Mixed separation interface: rigid or

flexible structure, air aperture, MPP…

3. Parallel structural and acoustic sound

transmission paths between acoustic media

Compound Panel Subsystem

Aperture with thin thickness assumption:

0 0( , , ) ( , , ) ( )aa a

pp x y z p x y z z z

z

0

0 0

ˆ1 ( , , ) (1 )nna a

z a

n z

p x y z aV

j z c

- Taylor series expansion:

- Cross-thickness velocity:

2 2

0

1( )

i j

a

i

aij a i a ja

nz aj S S

V jY dS dS

L s NF

- Aperture mobility:

- Panel mobility: 2 2 2

1

( )i j

p

i

pij p i p jp

mp p m pj s s

V jY dS dS

h s NF

Virtual panel treatment of an air aperture

Virtual Panel

0 0

0

0

a a

p p

mpp mpp

F V

F V

F V

a

p p-mpp

mpp- p mpp

Y

Y Y

Y Y

Description of a compound panel

Mobility matrix Excitation Response

Combine rigid/flexible structure, aperture, MPP into a single structural interface

Compound Panel Subsystem

A compound panel surrounded

by two acoustic media

Validation against FEM

Effective thickness criterion test:

• Percentage error between the proposed approach

and exact value:

• Criterion of provides satisfactory accuracy

• Criterion of fully guarantees the accuracy

( ) /vp bt btPE P P P

/ 4s

/16s

Compound Panel Subsystem – Thickness Criterion

Rectangular cavity with enclosed partial structure

Rigid/flexible and micro-perforated partition:

1. MPP brings a noticeable pressure balance

across the partition

2. MPP adds system damping by means of

energy dissipation through the holes

128Hz

128Hz

63Hz

Various Applications

Semi-infinite acoustic domain

Rigid baffleRigid baffle

Point sourceAcoustic enclosure

Partial flexible plateReceiving point

x

zy

1. The interface being treated as compound panel

can be any combination of structure and aperture

2. Sound scattering pattern can be clearly observed


Radiation from a partially covered enclosure


Effect of adding MPP absorbers:

• Internal MPP absorbers improve TL

• Absorption behavior is very complicated

• Require fully-coupled modeling tools

0.36m

0.84m

Interior domain

Exterior domain

Double-glazed ventilation window system Validation of the model against FEM

Interior and Exterior domains are infinite duct


Effect of additional MPPs


0.3m

Baffle

Baffle

MPP

MPP

Solid

Empty

MPP Solid

Reactive expansion chamber silencer

1. The proposed approach is more

computational efficient than FEM

2. Numerical studies provide silencer

design guidance

Application to Duct Silencer

Empty expansion chamber

Complex internal partitions

Hybrid silencers Effect of MPP

Complex silencer configuration with rigid/MPP internal partitions


Vibration of internal partitions attributed to thin structures may deteriorate the silencing effect—performance overestimated!

Experimental measurement:


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.

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.

Concluding Remarks

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

micro-perforates in vibro-acoustic systemsmicro-perforates in vibro-acoustic systems li cheng chair...

Documents