ABAQUS声学问题-利用ABAQUS声学建模问题

ModelingAcousticProblemsUsingABAQUSLecture3Structural-AcousticAnalysiswithABAQUSOverviewAcousticElementTypesMaximumElementSizeExternalMeshedDomainBoundaryConditionsLoadsExteriorProblemsusingInfiniteElementsAnalysisProceduresOutputStructural-AcousticAnalysiswithABAQUSAcousticElementTypesStructural-AcousticAnalysiswithABAQUSAcousticElementTypesAcousticelementsareavailableinlinearandquadraticinterpolation.ABAQUS/Standardhasfirst-andsecond-orderfullintegrationelements:Quadrilateralandtriangularforplanarandaxisymmetricdomains(AC2D3,AC2D4,AC2D6,AC2D8,ACAX3,ACAX4,ACAX6,ACAX8)Hexahedral,tetrahedral,andwedgeforthree-dimensionaldomains(AC3D4,AC3D6,AC3D8,AC3D10,AC3D15,AC3D20)One-dimensionalacousticlinkstomodelacousticchannels(AC1D2,AC1D3)Examples:Piping,ducts,smallopeningsbetweenlargeregionsStructural-AcousticAnalysiswithABAQUSAcousticElementTypesABAQUS/Explicithasfirst-orderreducedintegrationelements:Quadrilateralandtriangularforplanarandaxisymmetricdomains(AC2D3,AC2D4R,ACAX3,ACAX4R)Hexahedralandtetrahedralforthree-dimensionaldomains(AC3D4,AC3D8R)Structural-AcousticAnalysiswithABAQUSAcousticElementTypesAcoustic-structuralinterface(ASI)couplingelements(ABAQUS/Standardonly):Providethecouplingeffectsbetweenanacousticmeshandastructuralmesh.Canbedefinedtwodifferentways:UsercanexplicitlycreateASIelements.UsercanallowASIelementstobegeneratedinternallyandautomatically,usingTIEconstraintsbetweenthefluidandsolidsurfaces.TIEconstraintsareavailableforbothABAQUS/StandardandABAQUS/Explicitandwillbediscussedfurtherinthenextlecture.Structural-AcousticAnalysiswithABAQUSAcousticElementTypesAcousticinfiniteelements:AvailableinbothABAQUS/StandardandABAQUS/Explicit*.Providedforexteriorproblems.Havesurfacetopologyandaresimilartostructuralinfiniteelements.Generallydefinedonaterminatingsurfaceofaregionofacousticfiniteelements.Formulationisconsiderablymoreaccuratethanimpedance-typeboundaryconditionsforcomplexwavefields—ninthorderimplementation.CanbecoupleddirectlytoastructuralsurfaceusingTIEconstraints.Ingeneral,acousticinfiniteelementswillprovidehigheraccuracywhenusedinsteadofimpedance-typeboundariesatthesamedistancefromthestructure.*ForABAQUS/Explicit,thisrepresentsasignificantadvanceoverthepublishedliteratureoninfiniteelements.Structural-AcousticAnalysiswithABAQUSAcousticElementTypesElementselectionInterpolationorderSecond-orderelementsaregenerallymuchmoreaccuratethanfirst-orderacousticelementsforagivennumberofdegreesoffreedom.First-orderelementsareslightlyfasterandareincludedforconvenience.Bothfirst-andsecond-orderacousticmeshesworkwelltogetherwithstructuralmeshes.Structural-AcousticAnalysiswithABAQUSAcousticElementTypesElementshapeQuad/hexelementsareslightlymoreaccuratethantri/tetelements.Oftentri/tetelementsrequirelesseffortincreatingthemesh.GeneralcommentsTherearenoproblemsassociatedwithusingdifferentintegrationordersordifferentelementshapesonthefluidandsolidmeshes.ABAQUS/Explicitoffersreducedintegrationelementswithautomatichourglasscontrol,makinghourglassingextremelyunlikely.Structural-AcousticAnalysiswithABAQUSAcousticElementTypesAcousticimportAcousticelementsmaybeimportedbetweenABAQUS/StandardandABAQUS/Explicit.Thisenablescoupledfluid-solidanalysessuchas:Eigenanalysis(ABAQUS/Standard)ofpost-shock(ABAQUS/Explicit)structures.Transientdynamic(ABAQUS/Explicit)analysisofsystemsunderstaticpreload(ABAQUS/Standard).TheinterfaceforacousticimportisidenticaltothatforgeneralimportinABAQUS.Structural-AcousticAnalysiswithABAQUSMaximumElementSizeStructural-AcousticAnalysiswithABAQUSMaximumElementSizeElementsizeRelatedtomaximumfrequency(orminimumwavelength)Higherfrequencyresponserequiressmallerelements.Wavelengthdecreaseswithincreasingfrequency,sothereisanupperfrequencylimitforagivenmesh.MaximumelementsizeForreasonableaccuracyatleastsixrepresentativeinternodalintervals(nmin)shouldfitintotheshortestacousticwavelengthofinterest.An“internodalinterval”isdefinedasthedistancefromanodetoitsnearestneighborinanelement.Structural-AcousticAnalysiswithABAQUSMaximumElementSizeForexample,themaximumelementsizeforalinearelementishalfthemaximumelementsizeforaquadraticelement.Usethefollowingrelationshipstodeterminethemaximuminternodaldistance(Lmax)orthemaximumvalidfrequency(fmax)foragivenmesh: wherecisthespeedofsoundandnministhenumberofinternodalintervals.Structural-AcousticAnalysiswithABAQUSMaximumElementSizeExample:Internodaldistancerequirementsforvariousfrequencies,assuming6intervalsperwavelength.Structural-AcousticAnalysiswithABAQUSMaximumElementSizeHowcanwetellfromtheresultsifthemeshistoocoarsetomodeltheproblemadequately?Ifyouareuncertainaboutthecorrectmeshrefinementtouseforacertainanalysis,itisgoodpracticetoperformadirectsteady-statedynamicsanalysisonasimplifiedmeshatthefrequenciesofinterestandobservetheresults.Thesolutionmayshowalargevariationinacousticpressure(POR)acrossafewelements.Constant-phasesurfacesshowtheprogressofthewavethroughthemedium.Highlyirregularphaseanglecontourlines,therefore,usuallyindicateinadequaterefinement.PhaseangleofafieldvariablecanbecreatedinABAQUS/Viewerusingtherealandimaginarypartsofthefieldvariable.Structural-AcousticAnalysiswithABAQUSMaximumElementSizeIllustration:UsingPhaseangleofPORtodetermineadequacyofmeshrefinement.Thephaseanglecontourontopshowstoomanywavelengthsforthediscretization:theseshowupasredtoblueshifts.Insomeareasthisisseenoveronlytwoelements.Onthebottomthephaseanglecontourisrepresentativeofanadequaterefinement.Structural-AcousticAnalysiswithABAQUSMaximumElementSizeLarge-domainacousticproblemsIfthefluidregioncontainsmanywavelengths,“pollutionerror”duetocumulativephaseerrorsmaynecessitatehigherrefinement.Veryhigherrorsoccurespeciallywhenpollutionaffectsreverberant(closed)systems:phaseerrorsresultinquitedifferentmodalimpedances.Example:17-wavelengthacousticductStructural-AcousticAnalysiswithABAQUSMaximumElementSizeConnectingfluidandstructuraldomainsWavespeedsusuallydifferbetweenmedia.Consequently,atagivenfrequencyonemediumwillnaturallyrespondwithashorterwavelengththantheother.Example1:A2mm-thickflatsteelplatehasaflexuralwavelengthof0.45mat100Hz.Airhasanacousticwavelengthof3.3mat100Hz.Structural-AcousticAnalysiswithABAQUSMaximumElementSizeThesenaturalwavelengthssuggesttheelementsizesappropriateforafiniteelementmodelinganalysis.However,coupledsystemscanexhibit,inthevicinityofthemediaboundary,vibrationsattheshorterofthetwonaturalwavelengthsinbothmedia.Therefore,ifdetailsofthecoupledsolutionareimportant,bothmeshesmustbefineenoughtoresolvetheslow-mediumwavelengths.Thisfinezoneneedonlyextend~1(short)wavelengthintothefastmedium.Structural-AcousticAnalysiswithABAQUSMaximumElementSizeIfdetailsofthecouplingarenotimportant,thisrefinedzonecanbeomittedandhighlymismatchedmeshescanstillbecoupledinABAQUS.AccuratecouplingLessaccuratecouplingStructural-AcousticAnalysiswithABAQUSExternalMeshedDomainStructural-AcousticAnalysiswithABAQUSExternalMeshedDomainWhenastructureiscontainedwithinanacousticmediumofinfiniteextent,specialmeasuresmustbetakenontheouterboundary.AbsorbingboundaryconditionsAcousticinfiniteelementsWhenabsorbingboundaryconditionsareused,thesizeofanexternalmesheddomainisimportant.RelatedtofrequencycontentLowerfrequencyresponserequiresalargerdomaintobemeshedbutallowsalargerelementsize.Higherfrequencyresponserequiresasmallerelementsizebutallowsasmalleroverallmeshdiameter.MufflerExternalmesheddomainStructural-AcousticAnalysiswithABAQUSExternalMeshedDomainForexteriorproblemstheradiationconditionsconvergetotheexactsolutionwhenthe“standoff”distance,r1(distancefromthesourcetotheboundary),approachesinfinity.Greaterstandoffdistancespermitimprovedaccuracy.Foragivenmaterialandfrequencyofinterest,therequiredstandoff,r1,isgivenbythefollowingrelationship: wheremministhenumberofwavelengthsfromsourcetoboundary.Valuesof

mmingreaterthan1/3arerecommended.Structural-AcousticAnalysiswithABAQUSExternalMeshedDomainExample:Minimumstandoffdistanceforvariousfrequencies,assumingastandoffdistanceof1/3wavelength.Structural-AcousticAnalysiswithABAQUSExternalMeshedDomainExample:Mufflercritical

r1

distancesMinimumfrequencyofinterest:

170

HzCorrespondingwavelength:

~2000

mmFor

r1=1/3

(maxwavelength):

r1

=

667

mmStructural-AcousticAnalysiswithABAQUSExternalMeshedDomainComputationalrequirementsforexternaldomainsDependonboththeradiationboundarystandoffdistance,

r1;theinternodaldistance,nmin;andthefrequencyrange.Thetotalnumberofnodes,N,inthemodelcanbeapproximatedbythefollowingexpression: wheredisthespatialdimension(one-dimensional,two-dimensional,orthree-dimensional),nministhenumberofnodesrequiredperwavelength,andmministhenumberofwavelengthsdesiredfromsourcetoboundary.Structural-AcousticAnalysiswithABAQUSExternalMeshedDomainUsingoursuggestednumberstheexpressionforthreedimensionsbecomesThisexpressionshowstherelationshipbetweenbandwidthoffrequenciesandmodelsize.Asthefrequencyrangeofinterestincreases,themodelsizeincreasesrapidly.Structural-AcousticAnalysiswithABAQUSExternalMeshedDomainControllingmeshsizeforexternalproblemsBecauseofthestrongdependenceofthemeshsizeonthefrequencyrange,splittingtherangecanconsiderablyreducethecomputationaleffort.Theoptimalsplitofaband[fmin,fmax]isinto[fmin,f1]and[f1,fmax],wheref1=(fmin*fmax)1/2.Theneachnewmeshwillhaveasize

N~(fmax/fmin)d/2.Usingtheparametersofthepreviousexample:Structural-AcousticAnalysiswithABAQUSBoundaryConditionsStructural-AcousticAnalysiswithABAQUSBoundaryConditions:OverviewBoundaryconditionsOnlyoneboundaryconditionshouldbeappliedtoagivenregion(exceptatastructural-acousticinterface).Threetypesofacousticboundaryconditions:NaturalboundaryconditionRequiresnouserinput(sameasarigidwallaroundthefluid).ImpedanceModelslosseffectsbetweenacousticmediaandsolids.Alsomodelsacousticenergythatleavesthemeshthroughanonreflectingboundary.Availableforplanarwaves(default)andsimpledomainshapessuchascylinders,ellipses,etc.AppliedacousticpressureDefinethebasicsolutionvariableacousticpressure.Structural-AcousticAnalysiswithABAQUSBoundaryConditions:NaturalNaturalboundarycondition:reflectiveAcousticenergydoesnotleavethemesh—itreflectsbackintothemeshfromtheboundary.Thisconditionmodelsanacousticmediumborderedbyastationaryrigidwallorasymmetryplane.Accelerationoftheacousticmediumnormaltotheboundaryiszero;therefore,thepressuregradientnormaltotheboundaryisalsozero.ZeropressuregradientnormaltothewallpStructural-AcousticAnalysiswithABAQUSBoundaryConditions:NaturalWhatisthenaturalboundaryconditionusedtomodel?PurelyacousticregionboundaryExample:Carinteriornaturalfrequencyextractionwithnocouplingtothestructureofthecar.Usingthenaturalboundarycondition,thecomponentsofthecarinterioraretreatedasrigid,andtheycompletelyreflectbackallacousticenergy.Thissituationisanidealization,becauseitemssuchasthecarpetandtheseatsabsorbsomeamountofacousticenergy.Example:Internalairofamuffler.Theopeningofthemufflerrequiresseparateradiationboundaryconditions.Example:Ductworksystem.Theopeningoftheductworkrequiresseparateradiationboundaryconditions.Structural-AcousticAnalysiswithABAQUSBoundaryConditions:NaturalSymmetryregionExample:Tankinteriormodeledwithone-eighthsymmetry.Eachofthesymmetryregionsusesthenaturalboundarycondition.Noadditionalboundarydefinitionisrequired.Cyclicsymmetryforacousticsisnotyetsupported.Tetrahedralelementmodelwithone-eighthsymmetryStructural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceImpedanceboundaryconditionPrimarilyusedinthefollowingscenarios:Boundaryofapurelyacousticregion,wheretheeffectofanadjoiningstructureisintroducedthroughtheimpedance,withoutmodelingthestructure,suchasairinacarpetedroom.Atastructural-acousticinterfacetosimulateimperfectlossycouplingbetweenthetwomedia,suchasbetweenatransducerprobeandhumantissue.Structural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceAttheboundarybetweenameshedacousticregionandtheunmeshedacousticregionsurroundingittosimulatereflectionlessradiationtoinfinity,suchasmodelingtheeffectofanopensun-roofontheinterioracousticsofacar.Exterioracousticregionissolargeitdoesnotreflectawavebacktotheregionofinterest.Suchproblemscanalsobeaddressedusingacousticinfiniteelements,whichwillbediscussedinmoredetailshortly.Otherexamples:OpeningattheendofamufflerOpeningattheendofductworkSpeakerradiatingintoaroomStructural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedancePrescribedimpedanceatafluidboundarySomelosseffectsbetweenacousticmediaandsolids(orarigidwall)canbemodeledbyaspecifiedimpedanceattheinterface(e.g.,carpets,linings,coatings).TheimpedanceZ(f)isanalgebraicrelationshipbetweenthesteady-statevelocityandthepressureattheinterface.InABAQUSthecomplex-valuedZ(f)isspecifiedusingtherealandimaginarypartsoftheacousticadmittance,1/[Z(f)]:Structural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceRadiatingboundaryconditions(definedusingimpedance)Acousticenergyleavesthemeshthrougha“quiet”ornonreflectingboundary.Forplanewavesnormallyincidentonaplanarboundary,theimpedanceisImpedance,Z,isdefinedastheratioofacousticpressure,p,toassociatedparticlespeed,Impedanceisgenerallyacomplexquantityinsteady-statedynamics.Structural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceDefaultradiatingboundaryconditionsareexactonlyforplanewavesnormallyincidenttoaplanarboundary.Ingeneralcasestheyareanapproximation:acousticwavesaretransmittedacrosstheboundarywithasmallamountofreflection.Thedefaultradiatingboundaryconditionsmustberelativelyfarawayfromtheacousticsourcestobeaccurateforgeneralproblems

(>1wavelength).ABAQUSinternallycalculatesthecorrectimpedanceparameterstoapproximateanonreflectingboundary.Alternatively,youcanspecifyimpedancepropertiesdirectly,althoughtheyarenottrivialtocalculateforcomplexgeometries.Structural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceUsage:ABAQUSKeywordsThefollowingoptionscanbeusedtoprescribeanimpedanceboundarycondition: *SIMPEDANCE

surfacename,propertyname or *IMPEDANCE elementset,

impedancetype

(facelabel),propertynameTospecifytheimpedanceproperties,usethe*IMPEDANCEPROPERTYoption: *IMPEDANCEPROPERTY,NAME=propertyname 1/k1,

1/c1,

frequency ...Ifthepropertynameisomittedfroma*SIMPEDANCEor*IMPEDANCEdataline,thedefaultplanewaveabsorbingimpedancepropertiesareassumed.Structural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceUsage:ABAQUS/CAECurrently,theimpedance-relatedoptionsarenotsupportedbyABAQUS/CAEandmustbeaddedtothemodelviatheKeywordsEditor.*IMPEDANCEPROPERTYismodeldata*SIMPEDANCEishistorydataStructural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceAlternativestothedefaultradiatingboundarycondition.Defaultconditionrequirestheboundarytobefarfromthesourceforaccuracy.Predefined-shaperadiatingboundaryconditionsallowamoreaccuratesolutionwithasmallermeshedregion.Bestchoices:circular(two-dimensional)orspherical(three-dimensional)farfromthesource.Usage: *IMPEDANCEPROPERTY,TYPE=CIRCULARorSPHERE,NAME=propertyname r1

(radiusoftheboundary) *SIMPEDANCE

surfacename,

propertynameStructural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceExample:AcousticRadiationofaMufflerExteriorair(cylindricalsurface):circularabsorbingboundary*IMPEDANCEPROPERTY,NAME=QUIET,TYPE=CIRCULAR1000,*SIMPEDANCECYL_EXT,QUIETExteriorair(frontandbackfaces):planewaveabsorbingboundary*SIMPEDANCEFACE_EXTBoundaryisarightcircularcylinderRadiusofthecylinderNote:onlyhalftheexteriorairisshownStructural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceAllradiatingboundaryconditionsareapproximateingeneral.Radiationboundaryconditionsconvergetotheexactsolutionastheboundaryconditionsbecomeinfinitelydistantfromtheradiatingstructure.Errorinexterioracousticanalysisiscontrolledbydiscretization(numberofelements)aswellasapproximateradiatingboundaryconditions.Inpractice,theseradiationconditionsprovideaccurateresultswhenthesurfaceisatleastone-thirdwavelengthawayfromthestructureatthelowestfrequencyofinterest.Insteady-statedynamicstheyautomaticallyincludefrequencydependenceifthevolumetricdragisfrequencydependent.Intransientdynamicsthevalueofvolumetricdragonthefirstdatalineisused.Structural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceTheseboundaryconditionsarespatiallylocal.Youcandefinetheexteriorboundarytoincludedifferentboundaryconditiontypesondifferentboundaries.Example:Cylindricalregionwithhemispheresateachend.Thecylindricalregionhasa“circular”boundaryconditionandthehemisphereshavea“sphere”boundarycondition.CircularSphereStructural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceOtheroptions:ellipse,prolatespheroid.Insomecasesasphericalboundarycanleadtoanoverlylargemeshedregion.Otherboundaryshapescanallowamoreefficientmodel.Theseoptionspermitflexibilitytoobtainanaccuratesolutionusingareasonablemeshedregion.Theyaresuperiortothedefaultradiationboundaryconditionsiftheboundaryisrelativelyclosetotheacousticsource.Theyallowtheusertomodeltheexteriordomainaccuratelywithfewerelementsthanrequiredwiththedefaultradiatingboundaryconditions.Structural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceSpecialcaseforplanewaves:Ifthewavefrontisplanar,anda*DYNAMICor*DYNAMIC,EXPLICITprocedureisused,itispossibletoinvoketheIMPROVEDPLANEradiatingcondition.Thisconditionallowstheradiatingboundaryconditiontobeexactforobliqueanglesofincidence.PlanarEnhancedplanarStructural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceUsage:ForTYPE=ELLIPTICALorPROLATESPHEROIDyoumustprovideadditionalinformationabouttheshape,location,andorientationoftheradiationsurface.AcousticDomainEllipticalboundarycondition*IMPEDANCEPROPERTY,TYPE=ELLIPTICALor

PROLATESPHEROID,NAME=propertynamesemimajoraxis,

eccentricity,

{locationofcenter},{majoraxisvector}*SIMPEDANCE

surfacename,

propertynameStructural-AcousticAnalysiswithABAQUSBoundaryConditions:ImpedanceExample:Ellipticalboundaryconditioninafluidwithvolumetricdraginatransientanalysis(*DYNAMIC).Thepressureamplitudesare“clipped”toemphasizetheoutwardpropagation.Thecircularregioncontainsanonsymmetricshellstructure(notshown).Atthetimeshown,thewaveshavepropagatedbeyondtheboundary.Althoughthefieldisrathercomplexspatially,thesolutionwiththeellipticalboundaryconditionisnearlyindistinguishablefromthelarge-diameterreferencesolutionontheleft.Structural-AcousticAnalysiswithABAQUSBoundaryConditions:AcousticPressurePrescribedacousticpressureboundaryconditionPrescribedacousticpressureisaboundarycondition(*BOUNDARY)becauseitisthebasicvariableintheacousticmedium(acousticpressure—degreeoffreedom8).Prescribingazerovalueforthepressurerepresentsa“freesurface.”Thesurfaceofwateradjoiningaircouldbemodeledasafreesurfaceifgravityisneglected.Prescribinganonzerovalueforthepressurerepresentsapointsourceofsound.Insteady-stateanalysisLOADCASE=1referstothein-phase(real)partofthepressure(default)andLOADCASE=2referstotheout-of-phase(imaginary)partofthepressure.Structural-AcousticAnalysiswithABAQUSBoundaryConditions:AcousticPressureExample:AcousticRadiationofaMuffler*BOUNDARYINLET,8,8,1.0E-6LOADCASE=1bydefaultSetINLETInteriorairinlet:prescribedacousticpressureStructural-AcousticAnalysiswithABAQUSLoadsStructural-AcousticAnalysiswithABAQUSLoadsABAQUSconventionsBoundaryconditionisthespecificationofthebasicsolutionvariable.Loadistheconjugatetothebasicsolutionvariable.Example:Inlinearstaticsolidmechanicsonestatementoftheequilibriumequationis whereKisthematerialstiffnessmatrix,uisthedisplacementvector,andfistheloadvector.Thebasicsolutionvariableisuandtheconjugateisf.Structural-AcousticAnalysiswithABAQUSLoadsLoad(volumetricacceleration)istheconjugateofthebasicsolutionvariable(acousticpressure).Loadcanbeappliedatthenodes(*CLOAD)asinwardvolumetricaccelerationsatnodesontheboundaryoftheacousticmedium.Aswithboundaryconditions,LOADCASE=1referstothein-phase(real)accelerationandLOADCASE=2referstotheout-of-phase(imaginary)acceleration.Distributedloadingforacousticelements,correspondingto*DLOAD,requirestheuseofthe*INCIDENTWAVEoption,whichwillbedescribedinlecture5.Structural-AcousticAnalysiswithABAQUSLoadsExample*Cload,loadcase=2,amplitude=OMEGADRIVEN-END,8,1.5006E-5SetDRIVEN-ENDStructural-AcousticAnalysiswithABAQUSLoadsUnderstandingloadsfromtheequilibriumequationsBasicstatementofequilibrium(forathree-dimensionalproblem):Volumetricconstitutivelaw

:Transientdynamics—rearrangeandscale:Structural-AcousticAnalysiswithABAQUSLoadsFiniteelementvariationalstatementfortransientdynamics:

(1)“Mass”matrix (3)“Stiffness”matrix

(2)“Damping”matrix (4)“Load”matrix:

(forequilibrium)TheloadisintegratedoverdS(thesurface);itisa“volumetric”acceleration.Structural-AcousticAnalysiswithABAQUSLoads“Load”details/exceptions:Loadterm(forconcentratedload,*CLOAD):Ifvolumetricdragispresent,theequilibriumequationattheboundaryisIntransientdynamics*CLOADspecifiesF0directly.TheactualphysicalparticleaccelerationduetospecifiedF0isreducedbyr.Thelosstothevolumetricdragtermisdroppedatboundariesbetweenfluidandsolidmediaintransientproblems.accelerationlossduetovolumetricdrag

Structural-AcousticAnalysiswithABAQUSLoadsInsteady-statedynamicswecanwrite

orTherefore,forsteady-statedynamicsF0isalwaysequaltoacceleration,evenifthevolumetricdrag,r,isnonzero.F0forsteady-statedynamicsaccelerationStructural-AcousticAnalysiswithABAQUSLoadsExampleAhorizontal,flatrigidplateoscillatingverticallyimposesanaccelerationontheacousticfluid.Anacousticloadisequaltothisaccelerationtimesthesurfaceareaoftheplate.Theloadistheaccelerationofafluidparticleifthevolumetricdragiszero.fluidvibratingplateStructural-AcousticAnalysiswithABAQUSExteriorProblemsusingInfiniteElementsStructural-AcousticAnalysiswithABAQUSExteriorProblemsusingInfiniteElementsAsnotedearlier,exterioracousticsandshockproblemscanbeaddressedusingthefiniteelementmethod,providedspecialmeasuresaretakenontheouterboundary.InABAQUS,twoclassesofinfiniteboundarytreatmentsareavailable:Absorbingboundaryconditions(impedance)Acousticinfiniteelements.Theimpedanceconditionsarefairlygeneralandwerediscussedearlier.Recallthisapproachrequiresspecialattentiontothesizeoftheexterioracousticmeshdomain.Theuseofacousticinfiniteelementsforexteriorproblemsisthefocusofthisportionofthelecture.Structural-AcousticAnalysiswithABAQUSExteriorProblemsusingInfiniteElementsAcousticinfiniteelementsWiththeseelements,theexteriordomainisinterpretedasawave-bearingdomainidenticaltothatusedonthefiniteelementside.Aspecialchoiceofapproximationmethodsintheexteriorenforcethepropertiesofthesemi-infinitedomain.Theelementsaremoreaccuratethannonreflectingboundaries—ninth-orderapproximationisused.Theycanbeapplieddirectlytostructure.Convergenceisobtainedbyincreasingthemeshdiameter.InfiniteelementsmayreplacemuchoftheexterioracousticmeshStructural-AcousticAnalysiswithABAQUSExteriorProblemsusingInfiniteElementsExample:Steady-State(harmonic)Theresultsatlowfrequency(ka

=

0.0049)obtainedwithalargefiniteelementmeshandabsorbingboundaryconditionsarecomparedtothoseobtainedusingacousticinfiniteelements.Theshellmesh:(5mradius,70mlength)isshownbelow.Acousticinfiniteelementsareapplieddirectlytothestiffenedshell.Structural-AcousticAnalysiswithABAQUSExteriorProblemsusingInfiniteElementsTheexterioracousticfiniteelementmesh(usingquadratictetr