tutorial fundamentals acoustics 1 structural part · structural vibrations – modes in beams and...
TRANSCRIPT
-
Structural‐Acoustics Tutorial
Part 1 ‐Fund
amentals
Dr. Step
hen A. H
ambric
ASM
E IM
ECE 2009
Orlando
, Florida
-
Overview
•Instructor
•Structural Vibratio
ns–Mod
es in
beams and plates
–Mob
ility
•Soun
d radiated
by structural waves
–Ra
diation efficiency
•Structural waves gen
erated
by im
pinging soun
d–Transm
ission
loss
•Brief introdu
ction to num
erical m
etho
ds–FE, B
E, SEA
-
Instructor
•Dr. Step
hen A. H
ambric
–App
lied Re
search Lab, Pen
n State University
–Also Professor in Pen
n States’ G
radu
ate Program in
Acoustics
–Associate Dire
ctor, Pen
n State Ce
nter fo
r Acoustics
and Vibration (CAV
)
•Accom
panying materials:
–Structural Acoustics Tutorials, Parts 1 and
2, from
Acoustics Toda
y magazine
–Dow
nload at www.ham
bricacou
stics.com
http://www.hambricacoustics.com/
-
Motivation
•Structures can
amplify
(and
atten
uate) sou
nd
sources substantially
Soun
d Source
Transfer Fun
ction
Soun
d at Receiver
dBdB
dB
-
Structural Acoustic
Transfer F
unctions
•Define transfer fu
nctio
n:
•How
is it defined
?
2rad
P F
2 22
2ρ
ρ=
rad
oo
ao
rd
oPcAv
F
v Fc
PA
Soun
d po
wer
radiation
efficiency
Soun
d po
wer
App
lied force2
Surface
averaged
mob
ility
Fluid
impe
dance
-
Surface Averaged
Mob
ility
•Averaged
surface vibratio
n am
plitu
des caused
by know
n forces (m
obilitie
s)
2 2
v F
Peaks in th
e mob
ility
functio
n are caused
by
mod
es of reson
ance
-
Mod
es of R
eson
ance
•Supe
rposition
of forward and backward traveling waves
•Exam
ple for fle
xure of sim
ply supp
orted be
am:
•For o
ther bou
ndary cond
ition
s, waven
umbe
rs change,
e.g., for free
bou
ndaries:
22
22π
ωρ
ρ=
=m
mEI
mEI
kA
aA
22
2
(21)
4π
ωρ
−≅
mm
EIa
A
-
Mod
es of R
eson
ance
•Can also be compu
ted with
Finite
Element (FE)
mod
els or m
easured
–Measured and simulated
resonance freq
uencies seldom
match exactly
Glass plates
with
free
bo
undary
cond
ition
s
-
Mob
ility as a Summation of M
odes
•A structure’s m
obility fu
nctio
n is a sim
ple
series sum
mation of m
odal re
spon
ses to a
driving force
–Exam
ple: sim
ply supp
orted rectangular p
late
()
02
11
02
,sin
sin
4
1sin
sin
,(
)ω
ωπ
πω
ρπ
π∞
∞
==
⎛⎞
⎡⎤
⎡⎤
=×
×⎜
⎟⎢
⎥⎢
⎥⎛
⎞⎣
⎦⎣
⎦ ⎠⎝
⎜ ⎝−
⎟ ⎠
∑∑
mo
mo
nn
mx
ny
xy
ab
hab
xy
mx
ni
yv
aF
b
Mod
al m
ass
(fraction of
static m
ass)
Differen
ce
betw
een drive
and resonance
freq
uencies
Mod
e shape at
respon
selocatio
n
Mod
e shape at
drivelocatio
n
-
Mod
al Respo
nse Peaks
•Why isn’t m
odal re
spon
se infin
ite at
resonance freq
uencies?
•Be
cause
ωmnis com
plex, due
to dam
ping
–For lightly dam
ped system
s:
whe
re η
is th
e loss fa
ctor
()
22
1, ,
()
ωω
∝−
oo
mn
vxy
Fxy
12η
ωω
⎛⎞
≅+
⎜⎟
⎝⎠
mn
mn
i
-
Dam
ping
Mechanism
s
•Thin she
ets of rub
ber adhe
red
to th
e surface, or sand
wiche
d be
tween structures
•Adjoining
structures
–Co
upling losses
–Joint losses (friction)
•Soun
d radiation
-
Effects of Dam
ping
on
Mod
al Respo
nse Peaks
•Peak (and
‘anti‐p
eak’) amplitu
des de
crease with
increasing
dam
ping
–Mob
ility app
roache
s the mean levels of an infin
ite plate
How
can
mob
ility
of an infin
ite plate
be com
puted?
-
Infin
ite Structure M
obilitie
s•
A structure is effectively infin
ite whe
n waves re
flected
from
bou
ndaries are
very weak with
respect to the original
waves emanating from
a sou
rce
•For plates:
•Useful for:
–scaling mob
ilitie
s
–pe
rforming en
gine
ering estim
ates of
prop
osed
material changes
–Ch
ecking
mob
ility m
easuremen
t accuracy
()
inf
inf
1/
8ρ
==
YvF
Dh
-
Infin
ite Structure M
obility
Scaling Exam
ple
•Tw
o pane
ls with
identical geo
metries and
different m
aterials
–Lexan (plastic) and
Aluminum
-
Infin
ite Structure M
obility
Scaling Exam
ple
•Measured mob
ilitie
s of both pane
ls
-
Infin
ite Structure M
obility
Scaling Exam
ple
•Aluminum
panel m
obility scaled to th
at of Lexan / /ρ ρ
==
AlAl
AlAl
Lexan
Lexan
Lexan
Lexan
Ef
cf
cE
-
Radiation Efficiency
2ρ
rad
ooP cAv
ff c
1.0 σ (f)
Critical Frequ
ency, w
here
bend
ing and acou
stic
wavespe
edsmatch
Structure radiates
poorly
Peak ra
diation
σ = 1
-
Coincide
nce
Bend
ing waves are
dispersive, slower th
an
acou
stic waves at low
freq
uencies (sub
sonic),
and faster at h
igh
freq
uencies (sup
ersonic)
-
Radiating Flat Baffle
d Pane
lBe
low Coinciden
ce
Pressures
Odd
/Odd
>Odd
/Even >
Even
/Even
-
Radiating Flat Baffle
d Pane
l –Increasing
Frequ
ency
Intensities
(propo
rtional
to squ
are of
pressure)
-
Radiation Efficiency –Effects of
Coincide
nce Freq
uency Shifts
ff c
1.0 σ (f)
f c
Stiffer, lighter
structure with
faster waves
Highe
r σ
-
f c
Radiation Efficiency –Effects of
Coincide
nce Freq
uency Shifts
ff c
1.0 σ (f)
Flim
sier, heavier
structure with
slow
er waves
Lower σ
-
Soun
d Po
wer Transfer Functio
ns
•Co
mbining
surface averaged mob
ility with
radiation efficiency tells us ho
w well a
structure radiates sou
nd whe
n driven
by a
know
n force
-
(1,1) m
ode ‐>
‘loud
speaker’ m
ode
-
Acoustic
Waves Im
pinging on
Structures
-
Soun
d Transm
ission
Loss
of an Infin
ite Panel [
](
)(
)
()(
)
20
0
4
4
2
0
0
2
00
si
2sin
s
2s
n
ni
i
n
ρφ
τω
ρ
ωρ
η
ω
φ
φ
φ=
⎡⎤
++
⎣⎦
⎡⎤
−⎣
⎦
Dk
h
c
Dk
c
Dam
ping
im
portant a
t coincide
nce
Mass im
portant
below
coincide
nce
(mass law)
Stiffne
ss
impo
rtant a
bove
coincide
nce
Dips occur whe
n mass an
d stiffne
ss
term
s cancel
φ= 0
φ= 90
-
Soun
d Transm
ission
near C
oinciden
ce
-
Finite Element (FE) A
nalysis
•Used gene
rally to
mod
el
structures
–Plates, beams, and
solids
•Also sometim
es used to
mod
el acoustic
region
s,
usually inside
an ob
ject
•Many commercial
software packages
available
-
Boun
dary Element (BE
) Analysis
•Used to m
odel th
e bo
unda
riesof acoustic
region
s–Inside
or o
utside
a vibratin
g surface
•Once surface pressures and
velocitie
s are know
n, th
e acou
stic field anyw
here m
ay
be com
puted
•Some commercial softw
are
packages are available (not
as m
any as FE packages)
-
Coup
led FE/BE Analyses
•Im
pedance matrices of structures (from FE) and
acou
stic re
gion
s (from BE) m
ay be coup
led
–Enforce continuity of n
ormal fluctuating velocity along
bo
undary
-
Statistical Ene
rgy Analysis (SEA
)
•SEA m
odels the en
ergy exchange be
tween large
grou
ps of reson
ances in intercon
nected
structures and
acoustic
region
s–Usually used at high freq
uencies, whe
re m
ode coun
ts
are very high
–Exchange of e
nergy is m
odeled
statistically
•Get calculatio
ns averaged over large region
s, and
over w
ide
freq
uency (usually one
‐third octave) bands
–Fast com
putatio
ns, ind
epen
dent of increasing
freq
uency
–Va
‐One
softw
are
Structural-Acoustics Tutorial�Part 1 - FundamentalsOverviewInstructorMotivationStructural Acoustic Transfer FunctionsSurface Averaged MobilityModes of ResonanceModes of ResonanceMobility as a Summation of ModesModal Response PeaksDamping MechanismsEffects of Damping �on Modal Response PeaksInfinite Structure MobilitiesInfinite Structure Mobility �Scaling ExampleInfinite Structure Mobility �Scaling ExampleInfinite Structure Mobility �Scaling ExampleRadiation EfficiencyCoincidenceRadiating Flat Baffled Panel�Below CoincidenceRadiating Flat Baffled Panel – Increasing FrequencyRadiation Efficiency – Effects of Coincidence Frequency ShiftsRadiation Efficiency – Effects of Coincidence Frequency ShiftsSound Power Transfer FunctionsSlide Number 24Acoustic Waves Impinging on StructuresSound Transmission Loss �of an Infinite PanelSound Transmission near CoincidenceFinite Element (FE) AnalysisBoundary Element (BE) AnalysisCoupled FE/BE AnalysesStatistical Energy Analysis (SEA)
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