Computational Acoustics of Noise Propagation in Fluids - Finite and Boundary Element Methods

589 Pages·2008·12.98 MB·English

by  Steffen Marburg (auth.)

Computational Acoustics of Noise Propagation
in Fluids – Finite and Boundary Element Methods
·
Steffen Marburg Bodo Nolte
Editors
Computational Acoustics
of Noise Propagation
in Fluids – Finite and
Boundary Element Methods
With285 Figuresand 29 Tables
123
Editors:
SteffenMarburg(Ed.) BodoNolte(Ed.)
Institutfu¨rFestko¨rpermechanik ForschungsanstaltderBundeswehr
TechnischeUniversita¨tDresden fu¨rWasserschallundGeophysik
Helmholtzstraße10 KlausdorferWeg2–24
01062Dresden,Germany 24148Kiel,Germany
[e-mail] [e-mail]
ISBN 978-3-540-77447-1 e-ISBN 978-3-540-77448-8
DOI10.1007/978-3-540-77448-8
LibraryofCongressControlNumber:2008921125
(cid:2)c Springer-VerlagBerlinHeidelberg2008
Thisworkissubjecttocopyright. Allrightsarereserved,whetherthewholeorpartofthematerialis
concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,
reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication
orpartsthereofispermitted onlyundertheprovisions oftheGermanCopyrightLawofSeptember9,
1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsare
liableforprosecutionundertheGermanCopyrightLaw.
Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,
evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws
andregulationsandthereforefreeforgeneraluse.
TypesettingandProduction:LE-TEXJelonek,Schmidt&Vo¨cklerGbR,Leipzig,Germany
CoverDesign:eStudioCalamarS.L.,F.Steinen-Broo,Girona,Spain
Printedonacid-freepaper
987654321
springer.com
ForMa¨xi,Jolly& Milan,whowas theWDL1
1dasWunderdesLebens(TheWonderoflife)
Preface
Low noise constructionsreceiveincreasing attentionin highly industrializedcoun-
tries. Consequently,controlof noise emission challengesa growingcommunity of
engineers.Classically,noiseemissioniscontrolledexperimentallyutilizingthetrial
anderrormethodandengineeringexperience.Thedevelopmentofnumericalmeth-
odssuchasthefinite elementandtheboundaryelementmethodforlowfrequency
acousticproblemsandstatisticmethodsforhighfrequencyproblemsallowssimula-
tionofradiationandscatteringfromarbitrarygeometricobjects.
For low and mediumfrequencyproblems, classical approachesfor solution of
problemsofacousticsfavoranalyticalmethodsincludingFourierseriesapproaches.
Theseapproachesarequitepowerfulandtheyarestilldevelopedfurther.Inparticu-
lar,iforthogonaleigenfunctionsareusedasthebasisfunctionsoftheFourierseries,
theyconvergerapidly.However,ifthegeometryoftheradiatororscattererbecomes
morecomplicated,Fourierseriesbecomeimpracticaltouse.Inthesecases,numer-
ical methodscan be used more conveniently.The easiest and most straightforward
approachconsistsofthefinitedifferencemethod.However,finitedifferencemethods
sufferfromanumberofspecificproblemssuchasmeshrestrictionsanddispersion.
Alternatively,finiteelementandboundaryelementmethodsuseamorecomplicate
mathematicalformulationbutcanbeappliedinaverygeneralway.
This book deals with finite element and boundary element methods for acous-
ticproblems.Although,thetitlecontainstherestrictionoftheacousticsoffluids,a
numberofchaptersconsidersolidstructuresaswell.Theeditioncomprises21chap-
ters.Thefirstone,i.e.Chapter0,isaconceptchapter.Itstartswiththederivationof
theharmonicwaveequationfromthefundamentalrelationsofcontinuummechan-
ics.Itisfollowedbytenchaptersonfiniteelementmethodsandanothertenchapters
onboundaryelementmethods.ThereaderisreferredtoChapter0andSection0.6,
cf. pages 20–22, to survey the remaining chapters and discuss them related to the
formulationswhicharegiveninChapter0.
VIII Preface
Thisisabookonnumericalmethods.InthefirstvolumeofhisseriesTheHitch-
hiker’s Guide to the Galaxy,2 Douglas Adams formulates “the ultimate answer to
life,theuniverse,andeverything.”Itisanumericsolution:42,evaluatedbythecom-
puterDeepThought.ACPUtimeof≈2.37×1014seconds(7.5Millionyears) was
requiredtoachievethisinterestingresult.Thisbookonnumericalmethodscontains
contributionswrittenby42authors.Thenumberof42mightindicatethatitcovers
a wide range of topics of computationalacoustics. However,the readershould not
expecttheultimateanswertotheproblemsofcomputationalacousticsingeneral.It
tooktheeditors≈20months(≈5.2×107seconds)ofmanualworkfromtheideato
thefinalversionofthebook.Therearemanyreasonswhythisbookhasbeencom-
pleted much faster than the evaluationof Deep Thought.Maybe this was achieved
becausetheoverallcontentisless generalthantheultimateanswertolife,the uni-
verse, and everything. Probably, the major reason for the successful and efficient
completionconsistsinthewillinglycollaborationofallauthorstosupplytheeditors
withtheircontributions.Theeditorswishtoacknowledgethatithasbeentheirgreat
pleasuretoworktogetherwithallauthors.
A number of other persons have been relevant for the successful completion
of this edition. First of all, we wish to mention Eva Hestermann–Beyerle of the
Springer–VerlaginHeidelberg.Itisworthmentioningthatsheencouragedtheedi-
torstostartwiththeireditorialwork.Moreover,EvaHestermann–Beyerlehascontin-
uouslysupervisedtheprogressoftheeditionandprovidedtheeditorswithnumerous
valuableadvice.
TheeditorswishtothanktheirclosecolleaguesattheInstituteofSolidMechan-
ics at Technische Universita¨t Dresden and at the Federal Armed Forces Underwa-
terAcousticsandMarineGeophysicsResearchInstitutefortheirpatienceandtheir
support.Therearemanyotherswhocontributedtothesuccessfulcompletionofthis
work.Itseemstobeimpossibletomentionallofthem.However,theeditorsarevery
thankfulforeverysingleassistanceinduringthepreparationofthisbook.
DresdenandKiel, SteffenMarburg
October2007 BodoNolte
2DouglasAdams’TheHitchhiker’sGuidetotheGalaxywasoriginallypublishedin1979
byPanBooksLtd.,London.
Contents
0 AUnifiedApproachtoFiniteandBoundaryElementDiscretizationin
LinearTime–HarmonicAcoustics
S.Marburg,B.Nolte............................................... 1
PartI FEM:NumericalAspects
1 Dispersion,Pollution,andResolution
I.Harari ........................................................ 37
2 DifferentTypesofFiniteElements
G.Cohen,A.Hauck,M.Kaltenbacher,T.Otsuru......................... 57
3 MultifrequencyAnalysisusingMatrixPade´–via–Lanczos
J.P.Tuck–Lee,P.M.Pinsky,H.L.Liew................................ 89
4 ComputationalAeroacousticsbasedonLighthill’sAcousticAnalogy
M.Kaltenbacher,M.Escobar,S.Becker,I.Ali...........................115
PartII FEM:ExternalProblems
5 ComputationalAbsorbingBoundaries
D.Givoli ........................................................145
6 PerfectlyMatchedLayers
A.Bermu´dez,L.Hervella–Nieto,A.Prieto,R.Rodr´ıguez ..................167
7 InfiniteElements
R.J.Astley.......................................................197
8 EfficientInfiniteElementsbasedonJacobiPolynomials
O.vonEstorff,S.Petersen,D.Dreyer .................................231
PartIII FEM:RelatedProblems
X Contents
9 Fluid–StructureAcousticInteraction
A.Bermu´dez,P.Gamallo,L.Hervella–Nieto,R.Rodr´ıguez,D.Santamarina...253
10 EnergyFiniteElementMethod
R.Bernhard,S.Wang ..............................................287
PartIV BEM:NumericalAspects
11 DiscretizationRequirements:HowmanyElementsperWavelength
areNecessary?
S.Marburg ......................................................309
12 FastSolutionMethods
T.Sakuma,S.Schneider,Y.Yasuda....................................333
13 Multi–domainBoundaryElementMethodinAcoustics
T.W.Wu ........................................................367
14 WaveguideBoundarySpectralFiniteElements
A.Peplow .......................................................387
PartV BEM:ExternalProblems
15 TreatingthePhenomenonofIrregularFrequencies
S.Marburg,T.W.Wu ..............................................411
16 A Galerkin–type BE–formulation for Acoustic Radiation and
ScatteringofStructureswithArbitraryShape
Z.S.Chen,G.Hofstetter,H.Mang....................................435
17 AcousticalRadiationandScatteringaboveanImpedancePlane
M.Ochmann,H.Brick .............................................459
18 TimeDomainBoundaryElementMethod
S.Langer,M.Schanz...............................................495
PartVI BEM:RelatedProblems
19 CouplingaFastBoundaryElementMethodwithaFiniteElement
FormulationforFluid–StructureInteraction
L.Gaul,D.Brunner,M.Junge .......................................519
20 Inverse Boundary Element Techniques for the Holographic
IdentificationofVibro–AcousticSourceParameters
J.–G.Ih .........................................................547
Index...........................................................573
List of Contributors
Irfan Ali Friedrich–Alexander– HaikeBrickTFHBerlin–University
Universita¨t Erlangen–Nu¨rnberg, of AppliedSciences, Departmentof
Lehrstuhl fu¨r Stro¨mungsmechanik, Mathematics,PhysicsandChemistry,
Cauerstraße4,91058Erlangen,Ger- LuxemburgerStr. 10,13353Berlin,
many Germany
[e-mail]–erlangen.de brick@tfh–berlin.de
DominikBrunnerInstituteofApplied
R JeremyAstleyInstitute ofSound
andExperimentalMechanics,Pfaffen-
andVibrationResearch,Universityof
waldring9,70550Stuttgart,Germany
Southampton,Highfield,Southampton,
[e-mail]–stuttgart.de
SO171BJ,UnitedKingdom
[e-mail] ZhenshengChenAcousticsResearch
Institute, Austrian Academyof Sci-
ences,Wohllebengasse12–14,A–1040
StefanBecker Friedrich–Alexander–
Vienna,Austria
Universita¨t Erlangen–Nu¨rnberg,
Lehrstuhl fu¨r Stro¨mungsmechanik, [e-mail]
Cauerstraße4,91058Erlangen,Ger-
Gary Cohen INRIA, Domaine de
many
Voluceau, Rocquencourt– BP 105,
[e-mail]–erlangen.de 78153LeChesnayCedex,France
[e-mail]
AlfredoBermu´dezDepartamentode
DanielDreyerHanseWohnbauGmbH,
Matema´tica Aplicada,Universidade
Birkenweg15,D–22850Norderstedt,
de Santiago de Compostela, 15782
Germany
SantiagodeCompostela,Spain
daniel.dreyer@h–wb.de
[e-mail]
Max EscobarFriedrich–Alexander–
RobertBernhardPurdueUniversity, Universita¨t Erlangen–Nu¨rnberg,
HovdeHall, 610PurdueMall, West Lehrstuhlfu¨rSensorik,Paul–Gordan–
Lafayette,IN47907,USA Straße3/5,91052Erlangen,Germany
[e-mail] [e-mail]–erlangen.de
XII ListofContributors
OttovonEstorffInstituteofModelling Jeong–GuonIhCentreforNoiseand
andComputation,HamburgUniversity VibrationControl(NoViC),Department
of Technology, Denickestraße 17, of Mechanical Engineering,Korea
D–21073Hamburg,Germany Advanced Institute of Science and
estorff@tu–harburg.de Technology(KAIST),ScienceTown,
Daejeon305–701,Korea
[e-mail]
Pablo Gamallo Departamento de
Matema´ticaAplicadaII,Universidade Michael JungeInstitute of Applied
deVigo,36310Vigo,Spain andExperimentalMechanics,Pfaffen-
[e-mail] waldring9,70550Stuttgart,Germany
[e-mail]–stuttgart.de
LotharGaulInstituteofAppliedand
Sabine LangerInstitute of Applied
ExperimentalMechanics, Pfaffen-
Mechanics, Technical University
waldring9,70550Stuttgart,Germany
Clausthal, Adolph–Roemer-Str.2a,
[e-mail]–stuttgart.de 38678Clausthal–Zellerfeld,Germany
s.langer@tu–clausthal.de
DanGivoliDepartmentofAerospace
Haw–Ling Liew Department of
Engineering,Technion,Haifa32000,
MechanicalEngineering,Faculty of
Israel
MechanicsandComputation,Stanford
[e-mail]
University,Stanford,CA,94305,USA
[e-mail]
IsaacHarariFacultyofEngineering,
ManfredKaltenbacher Friedrich–
TelAvivUniversity,69978RamatAviv,
Alexander–Universita¨tErlangen–
Israel
Nu¨rnberg,Lehrstuhl fu¨r Sensorik,
[e-mail]
Paul–Gordan–Straße3/5,91052Erlan-
gen,Germany
AndreasHauckFriedrich–Alexander– [e-mail]–erlangen.de
Universita¨t Erlangen–Nu¨rnberg,
HerbertMangInstituteforMechanics
Lehrstuhlfu¨rSensorik,Paul–Gordan–
of Materials and Structures,Vienna
Str.3/5,91052Erlangen,Germany
UniversityofTechnology,Karlsplatz
[e-mail]–erlangen.de
13,A–1040Vienna,Austria
[e-mail]
LuisHervella–NietoDepartamentode
Matema´ticas,UniversidadedaCorun˜a, Steffen Marburg Institut fu¨r
15707ACorun˜a,Spain Festko¨rpermechanik, Technische
[e-mail] Universita¨tDresden,01062Dresden,
Germany
[e-mail]–dresden.de
Gu¨nterHofstetterInstituteforBasic
SciencesinCivilEngineering,Univer- Bodo Nolte Forschungsanstaltfu¨r
sityofInnsbruck,Technikerstraße13, Wasserschall undGeophysik,24148
A–6020Innsbruck,Austria Kiel,Germany
[e-mail] [e-mail]