11/16/20

09IM

ECE2009‐13

423

1

Structural‐Acoustic Tutorial

Part II –Structural‐Acoustic

 Finite

 Elem

ent A

nalysis & Autom

otive 

App

lications

Dr. Shun

g H.(S

ue) Sun

gASM

E  IM

ECE 2009

Orlando

, Florida

11/16/20

09IM

ECE2009‐13

423

2

Overview

•Instructor

•Acoustic

 Finite

 Element A

nalysis

–FE Formulation of Equ

ations‐of‐Motion

–Cavity M

odal Analysis

–Flexible W

all Excita

tion (FRFs & Panel Participation)

•Acoustic

 Absorption & Interior Trim

–Acoustic

 Dam

ping

 Mod

els 

–Exam

ple Ve

hicle App

lications

•Structural‐Acoustic

 Finite

 Element A

nalysis 

–Co

upled Structural‐Acoustic

 FE Form

ulation

–Mod

al Respo

nse, M

odal and

 Panel Participation 

–Flexible W

all Cou

pling Effect 

–Ve

hicle Validation 

–Exam

ple Ve

hicle App

lication

11/16/20

09IM

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3

Instructor

•Dr. Shun

g H. (Sue) Sun

g–B.S. ‐Civil Engineering, N

ational Taiwan

 University

–M.S. &

 Ph.D. ‐

Aero & Astro Engr., Purdu

e  University

–Gen

eral M

otors R&

D Cen

ter –Technical Staff 32 years

–ASM

E Fellow, A

IAA, SAE, ASA

, INCE

  Mem

ber

•Major Research

–Structural‐acoustic

 finite elemen

t analysis for vehicle 

CAE N&V de

sign

–Ve

hicle and en

gine

 FE mod

eling for radiated

 noise 

pred

ictio

n–Po

wer flow

 FE metho

d for high

 freq

uency N&V Analysis

–Statistical re

gression

  ene

rgy metho

d for early vehicle 

N&V de

sign

11/16/20

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ECE2009‐13

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4

Major Sou

rce

11/16/20

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ECE2009‐13

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5

Engine

 Vibration

Vehicle Interior Noise Paths

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ECE2009‐13

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6

Vehicle Structural & Acoustic Mod

els

Vehicle Structural M

odel

Compa

rtmen

t Acoustic Mod

el

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11/16/20

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ECE2009‐13

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8

Acoustic Bo

unda

ry Con

dition

s

0=

∂∂ np0

=u

unp

−=

∂∂ρ1

wu=

aZpu=

TYPE

BO

UN

DA

RY

CO

ND

ITIO

N

AIR

PA

RTI

CLE

VE

LOC

ITY

0=

p

tpZ

np

air∂∂

−=

∂∂1

1 ρai

rZp

u=

0=

u

TYPE

AIR

PA

RTI

CLE

VE

LOC

ITY

tpZ

Z

wtp

Znp

waa

∂∂ ⎟⎟ ⎠⎞⎜⎜ ⎝⎛

+−

=

−∂∂

−=

∂∂

111

1 ρ

waa

ZpZp

wZp

u

+=

+=

tpZ

np

a∂∂

−=∂∂

1

1 ρ

BO

UN

DA

RY

CO

ND

ITIO

N

11/16/20

09IM

ECE2009‐13

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9

Compa

rtmen

t Cavity Mod

es

[]

[]

() {

}0

2=

−p

QH

ω

0=

∂∂ np

RIG

ID W

ALL

MO

DES

11/16/20

09IM

ECE2009‐13

423

10

SPL &  Pan

el Con

tributions 

Prescribed

 Structural Excitation

(a) Interior SPL Spatial Variation

(b) P

anel Con

tribution Po

lar D

iagram

1‐Ba

ck    

Windo

w

2‐Re

ar Floor

3‐Ro

of

4‐Windshield

5‐Re

ar She

lf

6‐Fron

t Floo

r7‐To

tal N

oise

40 Hz Structural Vibration

 for Shaker Excitation of 

Vehicle

Soun

d Pressure Level (SPL)

at the

 Driver’s Ear

FOR

CED

RES

PON

SE

{}

{}{

}dA

wq

T

oA

θ∫

=

[]

[]

() {

}}

{2

qp

QH

=−ω

w

[]

[]{

}{

}{

}{}{

}

∑=∫

=

=−

∑=

== L ii

iT

iAi

ii

L ii A

A

dAw

q

qp

QH

pp

10

21

,

,)

(

, θ

ω

SUM

MED

PA

NEL

FO

RC

ED R

ESPO

NSE

11/16/20

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ECE2009‐13

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11

Vehicle Interior Acoustic Trim

Hea

dlin

er

Floo

r Car

petin

g

Fron

t Sea

tsR

ear S

eats

Trun

k Tr

im

IP &

Das

h

Aco

ustic

Fin

ite E

lem

ent M

odel

Doo

r Trim

“Cor

rela

tion

of a

n A

cous

tic F

inite

Ele

men

t Mod

el o

f the

Aut

omob

ile

Pass

enge

r Com

part

men

t Usi

ng L

ouds

peak

er E

xcita

tion”

, S. H

. Sun

g,

D. J

. Nef

ske,

and

D. A

. Fel

dmai

er, A

SME

Pape

r IM

ECE2

007-

4273

5.

11/16/20

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ECE2009‐13

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12

Item

FEM

Mod

elin

g M

etho

dIm

plem

enta

tion

Mod

elin

g &

C

ompu

tatio

nO

vera

ll Aco

ustic

D

ampi

ngM

odal

Dam

ping

(Inte

rior L

oss

Fact

or/

Rev

erbe

ratio

n Ti

me)

Est

imat

ed o

r Mea

sure

d M

odal

Dam

ping

Freq

uenc

y D

epen

dent

Very

Fas

t

Vehi

cle

Sea

ts“H

eavy

Air”

Equ

ival

ent-

Aco

ustic

Mod

el3D

Aco

ustic

Ele

men

ts

Mat

ched

to T

est D

ata

Freq

uenc

y In

depe

nden

tVe

ry F

ast

Inte

rior T

rim

(incl

udin

g S

eats

)A

cous

tic Im

peda

nce

Mod

elC

AA

BS

F E

lem

ents

Mea

sure

d Im

peda

nce

Freq

uenc

y D

epen

dent

Med

ium

Fas

t

Inte

rior T

rim

(incl

udin

g S

eats

)E

quiv

alen

t-Aco

ustic

M

odel

ing

3D A

cous

tic E

lem

ents

Mea

sure

d Im

peda

nce

or

Por

oela

stic

Mat

eria

l Dat

a

Freq

uenc

y D

epen

dent

Med

ium

Fas

t

Inte

riror

Trim

(in

clud

ing

Sea

ts)

Por

oela

stic

Mat

eria

l M

odel

ing

Spe

cial

3D

Ele

men

t/Cod

e

Mea

sure

d P

oroe

last

ic

Mat

eria

l Pro

perti

es

(RAY

ON

, NO

VA,

AC

TRA

N, E

XE

L, e

tc)

Can

be

Tim

e C

onsu

min

g

Acoustic Dam

ping

 Mod

eling Metho

ds

11/16/20

09IM

ECE2009‐13

423

13

FIN

ITE

ELEM

ENT

MO

MEN

TUM

,C

ON

TIN

UIT

Y EQ

UAT

ION

S

EQU

ILIB

RIU

M

EQU

ATIO

N

FIN

ITE

ELEM

ENT

EQU

ATIO

NS

[]

{}{

}dA

NN

ZD

T

Aa

∫=

1

[]

[]

(){

}{}

[]{

} wA

qp

QH

T−

=−

2ω

[]

{}{

}Ω

∇∫

∇=

Ωd

NN

HT

01 ρ[]

{}{

}Ω

∫=

Ωd

NN

BQ

T

01

BO

UN

DA

RY

TYPE

wt

pZ

np

a−

∂∂

−=

∂∂

/1

/1 0ρ

pu

∇=

−01 ρ

BO

UN

DA

RY

CO

ND

ITIO

N

FIN

ITE

ELEM

ENT

MAT

RIC

ESAcoustic Im

peda

nce FE Formulation

{}{} p

tr

pT

θ=)

,(

{}{}p

u, p

Bp

div

00

1)

1(

=∇

ρ

[]

[]

(){

}[]{

}{}

[]{

} wA

qp

Di

pQ

HT

−=

+−

ωω2

2. F

LEXI

BLE

WA

LL

w –

wal

l sur

face

-nor

mal

dis

plac

emen

t

flexi

ble

wal

lai

r

wn

p−

=∂

∂/

1 0ρ

–ab

sorb

er

impe

danc

eaZ

abso

rber

air

4. A

BSO

RB

ER O

N F

LEXI

BLE

WA

LL

flexi

ble

wal

l

tp

Bu

div

∂∂

=−

/1 0

11/16/20

09IM

ECE2009‐13

423

14

[]

[]

() {

}[]{

}{} q

pD

ip

QH

=+

−ω

ω2

σγ

ρi

Zc

a+

=/

[]

{}{

}dA

NN

ZD

T

Aa

∫=

1

Mea

sure

d Im

peda

nce/

Adm

ittan

ce

Acoustic Im

peda

nce Mod

el App

lication

11/16/20

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ECE2009‐13

423

15

Acoustic Im

peda

nce Mod

el App

lication

AT 1

27 H

z

127

127

11/16/20

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ECE2009‐13

423

16

Equi

vale

nt-A

cous

ticTr

im M

odel

ing

Equi

vale

nt-A

cous

tic E

quat

ion-

of-M

otio

n

0)

()

(12

2=

+∇

ae

ae

pB

pω

ωω

ρa

ea

ui

np)

(ωωρ

−=

∂∂

)(

)(

)(

)(

)(

ωω

ρω

ωρ

ωe

ee

ec

Bc

Z=

=

Equi

vale

nt-A

cous

tic F

inite

Ele

men

t Equ

atio

n

[]

[]{

}{

} ao

ae

ae

qi

pQ

BH

ωω

ωω

ρ=

⎥⎥ ⎦⎤

⎢⎢ ⎣⎡−

)(

)(1

2

Effe

ctiv

e D

ensi

ty &

Bul

k M

odul

us fr

om Im

peda

nce

)(

/)

(tan

)(

)(

22

ωω

ωω

ρe

eB

lk

Z−

=

11/16/20

09IM

ECE2009‐13

423

17

Equi

vale

nt-A

cous

tic M

odel

App

licat

ion

Aco

ustic

Cav

ity F

E M

odel

Equ

ival

ent-

Aco

ustic

Sea

t Mod

els

Eff

ectiv

e M

ass D

ensi

ty &

B

ulk

Mod

ulus

from

M

easu

red

Impe

danc

e

)Re(

eρ

)Im(

eρ

)Re(

eB

)Im(

eB

1

23

4

5

6

11/16/20

09IM

ECE2009‐13

423

18

Dri

ver’

s Ear

Lou

dspe

aker

Pred

icte

d SP

L in

Pas

seng

er C

ompa

rtm

ent

(1)

Left

Fron

t

(2)

Rig

ht F

ront

(3)

Left

Rea

r(4

) R

ight

Rea

r

(5)

Left

Trun

k

(6)

Rig

ht T

runk

11/16/20

09IM

ECE2009‐13

423

19

)1()()(

00

00

⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧= ⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥ ⎦⎤

⎢⎢ ⎣⎡+ ⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥ ⎦⎤

⎢⎢ ⎣⎡+ ⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥⎥ ⎦⎤

⎢⎢⎢ ⎣⎡ −t

G

tF

pw

HAK

pw

D

C

pw

QAM

T

Coup

led Structural‐Acoustic Ana

lysis

Un‐Symmetric Form

Symmetric Form

qp=

)1()(~

)(

0

0

0

0

⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧=

⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥ ⎦⎤

⎢⎢ ⎣⎡

−+

⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥⎥ ⎦⎤

⎢⎢⎢ ⎣⎡

−+

⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥ ⎦⎤

⎢⎢ ⎣⎡

−t

G

tF

qw

H

K

qw

DA

AC

qw

Q

M

T

Let

and  integrate flu

id equ

ation with

 minus sign with

 

Structural‐Acoustic Co

uplin

g & Sym

metric Form

 Autom

ated

 in M

SC/N

ASTRA

N,  Altair R

ADIOSS,  othe

r software

[]

{}{

}dS

NA

T

S

T∫

=θ

Structural‐Acoustic Co

uplin

g

∫−=

td

GG

0)

(~

ττ

11/16/20

09IM

ECE2009‐13

423

20

Mod

al Respo

nse Solution

)2(0

0

00

002

⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧=

⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥⎥ ⎦⎤

⎢⎢⎢ ⎣⎡+

⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥⎥ ⎦⎤

⎢⎢⎢ ⎣⎡+

⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥⎥ ⎦⎤

⎢⎢⎢ ⎣⎡ −

−GF

hak

d

ci

qam

Tζξ

ζξω

ςξω

[][][

]ϕ

φA

aT

=

{}

[]{}

{}

[]{

}ζ

ψξ

φ=

=p

u,

Uncou

pled

 Structural &

 Acoustic Mod

e Tran

sformation 

)1.(

00

EqT

×⎥ ⎦⎤

⎢ ⎣⎡ψ

φ

Mod

al Frequ

ency Respo

nse Equa

tion

s

{}

[][

][]

⎣⎦

∑∑

==

==

N k

N kk

Ta

pA

Zp

11

}{

}]{

[ζ

φψ

ψ

Mod

e & Pan

el Participa

tion

{}

{}∑ =

==

L ikp

p1

}{

][

ζψ

Aco

ustic

Mod

es (L

Aco

ustic

Mod

es)

Stru

ctur

al M

odes

(MS

truct

ural

Mod

es)

Bou

ndar

y P

anel

(N P

anel

Grid

s)1

2])

[]

[[]

[(

][

−+

+−

=h

di

qZ a

ωω

{}

[][

]∑ =

==

M jj

ap

aZ

p1

}{

}]{

[ζ

ϕ

11/16/20

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ECE2009‐13

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21

Structural‐Acoustic Co

uplin

g Effect 

on Station

 Wagon

 Tailgate Mod

es

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ECE2009‐13

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22

Structural‐Acoustic Co

uplin

g Effect 

on Noise Respo

nse in a Box

TOP BO

X WALL VIBRA

TION

INSERTION LOSS (dB)

FREQ

UEN

CY (H

Z)

1/3 OCTAV

E BA

ND CEN

TER FREQ

UEN

CY (H

Z)

(a)  Uniform

 Noise Enviro

nment

Structural FE Mod

el 

of Aluminum

 Box                      

(1.6 m

m wall thickne

ss)

Interior Cavity

 FE Mod

el 

of  A

luminum

 Box 

(300

 x 150

 x 5 m

m)

RMS VIBRATION VELOCITY (dB)

SPL AT

 CEN

TER OF BO

X

11/16/20

09IM

ECE2009‐13

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23

Valid

ation of a Veh

icle Structural‐A

coustic 

System

 Finite Elem

ent Mod

el

“A S

truc

tura

l-Aco

ustic

Fin

ite E

lem

ent M

etho

d fo

r P

redi

ctin

g A

utom

otiv

e Ve

hicl

e In

teri

or R

oad

Noi

se,”

S. H

. Sun

g, D

. J.

Nef

ske,

D. A

. Fel

dmai

er, I

ME

CE

2009

-110

65, 2

009.

11/16/20

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ECE2009‐13

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24

Vehicle Structural & Acoustic Mod

els

11/16/20

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ECE2009‐13

423

25

Structural‐Acoustic Ve

hicle System

 Mod

el  

Develop

men

t & Solution Proced

ures

Dam

ping

11/16/20

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ECE2009‐13

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26

Finite Elemen

t Equa

tion

s‐of‐M

otion

Vehicle Structural System M

odel

Vehicle Structural‐Acoustic System

 FE Mod

el

Coup

led Trim

med

 Bod

y (1) a

nd Chassis (2

) Sub

system

 FE Mod

els

⎭⎬⎫⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧ ⎥ ⎦⎤⎢ ⎣⎡

+⎭⎬⎫

⎩⎨⎧ ⎥ ⎦⎤⎢ ⎣⎡

+⎭⎬⎫

⎩⎨⎧ ⎥ ⎦⎤⎢ ⎣⎡ −

)()(

00

00

tG

tF

pwHA

Kpw

DC

pwQ

AMT

⎭⎬⎫

⎩⎨⎧ = ⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥ ⎦⎤⎢ ⎣⎡

+−

−+

+ ⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥ ⎦⎤⎢ ⎣⎡ + ⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥ ⎦⎤

⎢⎢ ⎣⎡

21

21

122

12

1212

1

21

2

1

21

2

1

0

00

0

FFww

KK

KK

KK

ww

C

Cww

M

M

Compa

rtmen

t Acoustic Cavity M

odel

⎭⎬⎫⎩⎨⎧

=⎭⎬⎫

⎩⎨⎧ ⎥⎥ ⎦⎤

⎢⎢ ⎣⎡+ ⎭⎬⎫

⎩⎨⎧ ⎥ ⎦⎤⎢ ⎣⎡

+ ⎪ ⎭⎪ ⎬⎫

⎪ ⎩⎪ ⎨⎧ ⎥⎥ ⎦⎤

⎢⎢ ⎣⎡0

~~

00

0~

~o

ao

aao

oao

aoo

ao

aao

oao

qi

ppH

HH

Hpp

D

pp

QQ

QQ

ω

Compartmen

t Cavity

 (o) and

 Interior Trim (a

) Equ

ivalent‐Acoustic

 FE Mod

els

11/16/20

09IM

ECE2009‐13

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27

CPU Im

provem

ent with New

Hardw

are an

d AMLS Solver Techno

logy

1.0

10.0

100.0

1000.0

10000.0

HP 2008, A

MLS Solver

HP 2008, Tradition

al 

Solver

HP 2001, Tradition

al 

Solver 

CPU (in min)CP

U of S

tructural‐A

coustic Mod

el 

with 65

0K DOF 

Hardw

are

Improvem

ent

Solver 

Techno

logy

AM

LS –

Aut

omat

ed M

ulti-

Leve

l Sub

stru

ctur

ing

11/16/20

09IM

ECE2009‐13

423

28

Axle Shaker Excitation

11/16/20

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29

Tire Patch Excitation

11/16/20

09IM

ECE2009‐13

423

30

On‐Ro

ad Veh

icle In

terior Noise Respo

nse

(60 km

/h on Co

arse Roa

d) 

Veh

icle

Stru

ctur

al

Sys

tem

FE

Mod

el

Mea

sure

d C

oare

e R

oad

Pro

file

Inte

rior S

ound

Pre

ssur

e Le

vel a

t Fr

ont P

asse

nger

Ear

Loc

atio

n

50 K

PH

11/16/20

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ECE2009‐13

423

31

App

lication of Structural‐A

coustic Ve

hicle 

System

 Finite Elem

ent Mod

el in

 Autom

otive 

Vehicle Design

11/16/20

09IM

ECE2009‐13

423

32

Stru

ctur

al F

E M

odel

3-D

Aco

ustic

FE

Mod

el

Roa

d,Po

wer

trai

n,A

irbo

rne

Inpu

ts

Spea

ker,

Spee

ch,

Pres

sure

Inpu

ts

Pred

icte

dIn

teri

orN

oise

Leve

l

Mod

al a

ndPa

nel

Part

icip

atio

n

Mod

ify p

asse

nger

com

part

men

t

Mod

ify st

ruct

ure

Acc

epta

ble

Aco

ustic

Des

ign

Structural‐Acoustic Proced

ure

11/16/20

09IM

ECE2009‐13

423

33

FRF an

d Pane

l Polar Diagram

Rear Roo

f (1)

Middle Ro

of (2

)

Rear Floor (5

)

Fron

t Ro

of (3

)

43 H

z

Pan

el P

olar

Dia

gram

At 4

3 H

z

SP

L

11/16/20

09IM

ECE2009‐13

423

34

Mod

al and

 Pan

el Participa

tion

54 H

z48

Hz

34 H

z

Vehi

cle

Bod

y P

anel

Par

ticip

atio

n to

inte

rior r

oad

nois

e re

spon

se a

t 54

Hz

V=3

5 M

PH

11/16/20

09IM

ECE2009‐13

423

35

App

lication in Veh

icle Design

Dom

inant B

ody Mod

e Participation

Ove

rall

Noi

se R

educ

tion

-7

dBA

11/16/20

09IM

ECE2009‐13

423

36

Summary

•The

 structural‐a

coustic  finite elemen

t metho

d ha

s be

en 

establishe

d an

d valid

ated

 for mod

eling complex autom

otive 

vehicle system

s.

•Structural‐a

coustic mod

eling, autom

ated

 structural‐a

coustic 

coup

ling,  m

odal/pan

el participa

tion

, and

 AMLS are available in 

commercially available software (e.g., MSC/N

astran

, RADIOSS)

•Large structural‐a

coustic system

 mod

els are easily solved using 

advanced

 solver techno

logy and

 com

puter ha

rdware

•More research work is neede

d to re

presen

t interior trim

 and

 othe

r pa

ssen

ger compa

rtmen

t characteristics in th

e structural‐

acou

stic veh

icle system m

odel.

•Rob

ust a

nd stand

ardized de

sign

 procedu

res are requ

ired

 to 

facilitate no

ise an

d  vibration

 design in th

e early vehicle de

sign

 an

d de

velopm

ent stages.

11/16/20

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ECE2009‐13

423

37

References

1.“Sou

ndin

SmallE

nclosures,”

D.J.Nefske&

S.H.Sung

,Cha

pter

6in

Noise

and

Vibration

ControlEngine

ering,

2ndEdition,

I.L.

Ver&

L.L.

Berane

k,ed

s.,John

Wiley&Sons,200

5.2.

“ACo

upledStructural‐AcousticFinite

Elem

entM

odelForVe

hicleInterior

Noise

Ana

lysis,”S.

H.S

ung

&D.J.N

efske,

ASM

EJ.of

Vibration

,Stressan

dRe

liability

inDesign,Vo

l.10

6,No.

2,19

84.

3.“Com

pone

ntMod

eSynthe

sisof

aVe

hicleStructural‐AcousticSystem

Mod

el,”S.

H.Sun

g&D.J.N

efske,AIAAJourna

l,Vo

l.24

,No.

6,19

86.

4.“Correlation

ofan

AcousticFinite

Elem

entMod

elof

theAutom

obile

Passen

ger

Compa

rtmen

tUsing

Loud

speakerExcitation

,”S.

H.Sung

,D.J.Nefske&

D.A.

Feldmaier,ASM

EIM

ECE2007

‐42735,2007.

5.“AnEquivalent‐AcousticFinite

Elem

entM

etho

dforMod

elingSoun

dAbsorbing

MaterialsintheAutom

obile

Passen

gerCo

mpa

rtmen

t,”D.J.N

efske&S.H.Sun

g,ASM

ENCA

D20

08‐73026,2008.

6.“A

Structural‐AcousticFinite

Elem

entMetho

dforPred

icting

Autom

otive

VehicleInterior

Road

Noise,”S.

H.Sung

,D.J.Nefske,

&D.A.Feldmaier,ASM

EIM

ECE2009

‐11065,2009.