11/16/20
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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
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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
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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
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4
Major Sou
rce
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5
Engine
Vibration
Vehicle Interior Noise Paths
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6
Vehicle Structural & Acoustic Mod
els
Vehicle Structural M
odel
Compa
rtmen
t Acoustic Mod
el
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7
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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
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9
Compa
rtmen
t Cavity Mod
es
[]
[]
() {
}0
2=
−p
QH
ω
0=
∂∂ np
RIG
ID W
ALL
MO
DES
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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
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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.
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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
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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
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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
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Acoustic Im
peda
nce Mod
el App
lication
AT 1
27 H
z
127
127
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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−
=
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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
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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
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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
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09IM
ECE2009‐13
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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
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Structural‐Acoustic Co
uplin
g Effect
on Station
Wagon
Tailgate Mod
es
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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
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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.
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24
Vehicle Structural & Acoustic Mod
els
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25
Structural‐Acoustic Ve
hicle System
Mod
el
Develop
men
t & Solution Proced
ures
Dam
ping
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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
ω
Compartmen
t Cavity
(o) and
Interior Trim (a
) Equ
ivalent‐Acoustic
FE Mod
els
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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
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28
Axle Shaker Excitation
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29
Tire Patch Excitation
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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
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31
App
lication of Structural‐A
coustic Ve
hicle
System
Finite Elem
ent Mod
el in
Autom
otive
Vehicle Design
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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
09IM
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
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H.S
ung
&D.J.N
efske,
ASM
EJ.of
Vibration
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dRe
liability
inDesign,Vo
l.10
6,No.
2,19
84.
3.“Com
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ntMod
eSynthe
sisof
aVe
hicleStructural‐AcousticSystem
Mod
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g&D.J.N
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ofan
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Elem
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elof
theAutom
obile
Passen
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Compa
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,”S.
H.Sung
,D.J.Nefske&
D.A.
Feldmaier,ASM
EIM
ECE2007
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etho
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elingSoun
dAbsorbing
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rtmen
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efske&S.H.Sun
g,ASM
ENCA
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icting
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otive
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H.Sung
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