StructuralAcousticsTutorial

Part1Fund

amentals

Dr.Step

henA.H

ambric

ASM

EIM

ECE2009

Orlando

,Florida

Overview

Instructor

StructuralVibratio

nsMod

esin

beamsandplates

Mob

ility

Soun

dradiated

bystructuralwaves

Ra

diationefficiency

Structuralwavesgen

erated

byim

pingingsoun

dTransm

ission

loss

Briefintrodu

ctiontonum

ericalm

etho

dsFE,B

E,SEA

Instructor

Dr.Step

henA.H

ambric

App

liedRe

searchLab,Pen

nStateUniversity

AlsoProfessorinPen

nStatesG

radu

ateProgramin

Acoustics

AssociateDire

ctor,Pen

nStateCe

nterfo

rAcoustics

andVibration(CAV

)

Accom

panyingmaterials:

StructuralAcousticsTutorials,Parts1and

2,from

AcousticsToda

ymagazine

Dow

nloadatwww.ham

bricacou

stics.com

http://www.hambricacoustics.com/

Motivation

Structurescan

amplify

(and

atten

uate)sou

nd

sourcessubstantially

Soun

dSource

TransferFun

ction

Soun

datReceiver

dBdB

dB

StructuralAcoustic

TransferF

unctions

Definetransferfu

nctio

n:

How

isitdefined

?

2rad

P F

2 22

2

=

rad

oo

ao

rd

oPcAv

F

v Fc

PA

Soun

dpo

wer

radiation

efficiency

Soun

dpo

wer

App

liedforce2

Surface

averaged

mob

ility

Fluid

impe

dance

SurfaceAveraged

Mob

ility

Averaged

surfacevibratio

nam

plitu

descaused

byknow

nforces(m

obilitie

s)

2 2

v F

Peaksinth

emob

ility

functio

narecaused

by

mod

esofreson

ance

Mod

esofR

eson

ance

Supe

rposition

offorwardandbackwardtravelingwaves

Exam

pleforfle

xureofsim

plysupp

ortedbe

am:

Foro

therbou

ndarycond

ition

s,waven

umbe

rschange,

e.g.,forfree

bou

ndaries:

22

22

=

=m

mEI

mEI

kA

aA

22

2

(21)

4

mm

EIa

A

Mod

esofR

eson

ance

Canalsobecompu

tedwith

Finite

Element(FE)

mod

elsorm

easured

Measuredandsimulated

resonancefreq

uenciesseldom

matchexactly

Glassplates

with

free

bo

undary

cond

ition

s

Mob

ilityasaSummationofM

odes

Astructuresm

obilityfu

nctio

nisasim

ple

seriessum

mationofm

odalre

spon

sestoa

drivingforce

Exam

ple:sim

plysupp

ortedrectangularp

late

()

02

11

02

,sin

sin

4

1sin

sin

,(

)

==

=

mo

mo

nn

mx

ny

xy

ab

hab

xy

mx

ni

yv

aF

b

Mod

alm

ass

(fractionof

staticm

ass)

Differen

ce

betw

eendrive

andresonance

freq

uencies

Mod

eshapeat

respon

selocatio

n

Mod

eshapeat

drivelocatio

n

Mod

alRespo

nsePeaks

Whyisntm

odalre

spon

seinfin

iteat

resonancefreq

uencies?

Be

cause

mniscom

plex,due

todam

ping

Forlightlydam

pedsystem

s:

whe

re

isth

elossfa

ctor

()

22

1, ,

()

oo

mn

vxy

Fxy

12

+

mn

mn

i

Dam

ping

Mechanism

s

Thinshe

etsofrub

beradhe

red

toth

esurface,orsand

wiche

dbe

tweenstructures

Adjoining

structures

Co

uplinglosses

Jointlosses(friction)

Soun

dradiation

EffectsofDam

ping

on

Mod

alRespo

nsePeaks

Peak(and

antip

eak)amplitu

desde

creasewith

increasing

dam

ping

Mob

ilityapp

roache

sthemeanlevelsofaninfin

iteplate

How

can

mob

ility

ofaninfin

iteplate

becom

puted?

Infin

iteStructureM

obilitie

s

Astructureiseffectivelyinfin

itewhe

nwavesre

flected

from

bou

ndariesare

veryweakwith

respecttotheoriginal

wavesemanatingfrom

asou

rce

Forplates:

Usefulfor:

scalingmob

ilitie

s

pe

rformingen

gine

eringestim

atesof

prop

osed

materialchanges

Ch

ecking

mob

ilitym

easuremen

taccuracy

()

inf

inf

1/

8

==

YvF

Dh

Infin

iteStructureM

obility

ScalingExam

ple

Tw

opane

lswith

identicalgeo

metriesand

differentm

aterials

Lexan(plastic)and

Aluminum

Infin

iteStructureM

obility

ScalingExam

ple

Measuredmob

ilitie

sofbothpane

ls

Infin

iteStructureM

obility

ScalingExam

ple

Aluminum

panelm

obilityscaledtoth

atofLexan / /

==

AlAl

AlAl

Lexan

Lexan

Lexan

Lexan

Ef

cf

cE

RadiationEfficiency

2

rad

ooP cAv

ff c

1.0 (f)

CriticalFrequ

ency,w

here

bend

ingandacou

stic

wavespe

edsmatch

Structureradiates

poorly

Peakra

diation

=1

Coincide

nce

Bend

ingwavesare

dispersive,slowerth

an

acou

sticwavesatlow

freq

uencies(sub

sonic),

andfasterath

igh

freq

uencies(sup

ersonic)

RadiatingFlatBaffle

dPane

lBe

lowCoinciden

ce

Pressures

Odd

/Odd

>Odd

/Even>

Even

/Even

RadiatingFlatBaffle

dPane

lIncreasing

Frequ

ency

Intensities

(propo

rtional

tosqu

areof

pressure)

RadiationEfficiencyEffectsof

Coincide

nceFreq

uencyShifts

ff c

1.0 (f)

f c

Stiffer,lighter

structurewith

fasterwaves

Highe

r

f c

RadiationEfficiencyEffectsof

Coincide

nceFreq

uencyShifts

ff c

1.0 (f)

Flim

sier,heavier

structurewith

slow

erwaves

Lower

Soun

dPo

werTransferFunctio

ns

Co

mbining

surfaceaveragedmob

ilitywith

radiationefficiencytellsusho

wwella

structureradiatessou

ndwhe

ndriven

bya

know

nforce

(1,1)m

ode>

loud

speakerm

ode

Acoustic

WavesIm

pingingon

Structures

Soun

dTransm

ission

Loss

ofanInfin

itePanel [

](

)(

)

()(

)

20

0

4

4

2

0

0

2

00

si

2sin

s

2s

n

ni

i

n

=

++

Dk

h

c

Dk

c

Dam

ping

im

portanta

tcoincide

nce

Massim

portant

below

coincide

nce

(masslaw)

Stiffne

ss

impo

rtanta

bove

coincide

nce

Dipsoccurwhe

nmassan

dstiffne

ss

term

scancel

=0

=90

Soun

dTransm

ission

nearC

oinciden

ce

FiniteElement(FE)A

nalysis

Usedgene

rallyto

mod

el

structures

Plates,beams,and

solids

Alsosometim

esusedto

mod

elacoustic

region

s,

usuallyinside

anob

ject

Manycommercial

softwarepackages

available

Boun

daryElement(BE

)Analysis

Usedtom

odelth

ebo

unda

riesofacoustic

region

sInside

oro

utside

avibratin

gsurface

Oncesurfacepressuresand

velocitie

sareknow

n,th

eacou

sticfieldanyw

herem

ay

becom

puted

Somecommercialsoftw

are

packagesareavailable(not

asm

anyasFEpackages)

Coup

ledFE/BEAnalyses

Im

pedancematricesofstructures(fromFE)and

acou

sticre

gion

s(fromBE)m

aybecoup

led

Enforcecontinuityofn

ormalfluctuatingvelocityalong

bo

undary

StatisticalEne

rgyAnalysis(SEA

)

SEAm

odelstheen

ergyexchangebe

tweenlarge

grou

psofreson

ancesinintercon

nected

structuresand

acoustic

region

sUsuallyusedathighfreq

uencies,whe

rem

odecoun

ts

areveryhigh

Exchangeofe

nergyism

odeled

statistically

Getcalculatio

nsaveragedoverlargeregion

s,and

overw

ide

freq

uency(usuallyone

thirdoctave)bands

Fastcom

putatio

ns,ind

epen

dentofincreasing

freq

uency

Va

One

softw

are

Structural-Acoustics TutorialPart 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 PanelBelow 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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