ABAQUS关于固有频率的提取方法.docx
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ABAQUS关于固有频率的提取方法.docx
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ABAQUS关于固有频率的提取方法
Abaqus固有频率提取
6.3.5 Naturalfrequencye*traction
Products:
Abaqus/Standard Abaqus/CAE Abaqus/AMS
References
∙"Procedures:
overview,〞
∙"Generalandlinearperturbationprocedures,〞
∙"Dynamicanalysisprocedures:
overview,〞
∙*FREQUENCY
∙"Configuringafrequencyprocedure〞in"Configuringlinearperturbationanalysisprocedures,〞 Section14.11.2oftheAbaqus/CAEUser'sManual
Overview
Thefrequencye*tractionprocedure:
∙performseigenvaluee*tractiontocalculatethenaturalfrequenciesandthecorrespondingmodeshapesofasystem;
∙willincludeinitialstressandloadstiffnesseffectsduetopreloadsandinitialconditionsifgeometricnonlinearityisaccountedforinthebasestate,sothatsmallvibrationsofapreloadedstructurecanbemodeled;
∙willputeresidualmodesifrequested;
∙isalinearperturbationprocedure;
∙canbeperformedusingthetraditionalAbaqussoftwarearchitectureor,ifappropriate,thehigh-performanceSIMarchitecture(see "UsingtheSIMarchitectureformodalsuperpositiondynamicanalyses〞in"Dynamicanalysisprocedures:
overview,〞 );and
∙solvestheeigenfrequencyproblemonlyforsymmetricmassandstiffnessmatrices;theple*eigenfrequencysolvermustbeusedifunsymmetriccontributions,suchastheloadstiffness,areneeded.
Eigenvaluee*traction
Theeigenvalueproblemforthenaturalfrequenciesofanundampedfiniteelementmodelis
where
isthemassmatri*(whichissymmetricandpositivedefinite);
isthestiffnessmatri*(whichincludesinitialstiffnesseffectsifthebasestateincludedtheeffectsofnonlineargeometry);
istheeigenvector(themodeofvibration);and
Mand N
aredegreesoffreedom.
When
ispositivedefinite,alleigenvaluesarepositive.Rigidbodymodesandinstabilitiescause
tobeindefinite.Rigidbodymodesproducezeroeigenvalues.Instabilitiesproducenegativeeigenvaluesandoccurwhenyouincludeinitialstresseffects.Abaqus/Standardsolvestheeigenfrequencyproblemonlyforsymmetricmatrices.
Selectingtheeigenvaluee*tractionmethod
Abaqus/Standardprovidesthreeeigenvaluee*tractionmethods:
∙Lanczos
∙Automaticmulti-levelsubstructuring(AMS),anadd-onanalysiscapabilityforAbaqus/Standard
∙Subspaceiteration
Inaddition,youmustconsiderthesoftwarearchitecturethatwillbeusedforthesubsequentmodalsuperpositionprocedures.Thechoiceofarchitecturehasminimalimpactonthefrequencye*tractionprocedure,buttheSIMarchitecturecanoffersignificantperformanceimprovementsoverthetraditionalarchitectureforsubsequentmode-basedsteady-stateortransientdynamicprocedures(see "UsingtheSIMarchitectureformodalsuperpositiondynamicanalyses〞in"Dynamicanalysisprocedures:
overview,〞 ).Thearchitecturethatyouuseforthefrequencye*tractionprocedureisusedforallsubsequentmode-basedlineardynamicprocedures;youcannotswitcharchitecturesduringananalysis.Thesoftwarearchitecturesusedbythedifferenteigensolversareoutlinedin Table6.3.5–1.
Table6.3.5–1Softwarearchitecturesavailablewithdifferenteigensolvers.
SoftwareArchitecture
Eigensolver
Lanczos
AMS
SubspaceIteration
Traditional
SIM
TheLanczossolverwiththetraditionalarchitectureisthedefaulteigenvaluee*tractionmethodbecauseithasthemostgeneralcapabilities.However,theLanczosmethodisgenerallyslowerthantheAMSmethod.TheincreasedspeedoftheAMSeigensolverisparticularlyevidentwhenyourequirealargenumberofeigenmodesforasystemwithmanydegreesoffreedom.However,theAMSmethodhasthefollowinglimitations:
∙AllrestrictionsimposedonSIM-basedlineardynamicproceduresalsoapplytomode-basedlineardynamicanalysesbasedonmodeshapesputedbytheAMSeigensolver.See "UsingtheSIMarchitectureformodalsuperpositiondynamicanalyses〞in"Dynamicanalysisprocedures:
overview,〞 ,fordetails.
∙TheAMSeigensolverdoesnotputepositemodaldampingfactors,participationfactors,ormodaleffectivemasses.However,ifparticipationfactorsareneededforprimarybasemotions,theywillbeputedbutarenotwrittentotheprinteddata(.dat)file.
∙YoucannotusetheAMSeigensolverinananalysisthatcontainspiezoelectricelements.
∙Youcannotrequestoutputtotheresults(.fil)fileinanAMSfrequencye*tractionstep.
Ifyourmodelhasmanydegreesoffreedomandtheselimitationsareacceptable,youshouldusetheAMSeigensolver.Otherwise,youshouldusetheLanczoseigensolver.TheLanczoseigensolverandthesubspaceiterationmethodaredescribedin"Eigenvaluee*traction,〞 Section2.5.1oftheAbaqusTheoryManual.
Lanczoseigensolver
FortheLanczosmethodyouneedtoprovidethema*imumfrequencyofinterestorthenumberofeigenvaluesrequired;Abaqus/Standardwilldetermineasuitableblocksize(althoughyoucanoverridethischoice,ifneeded).Ifyouspecifyboththema*imumfrequencyofinterestandthenumberofeigenvaluesrequiredandtheactualnumberofeigenvaluesisunderestimated,Abaqus/Standardwillissueacorrespondingwarningmessage;theremainingeigenmodescanbefoundbyrestartingthefrequencye*traction.
Youcanalsospecifytheminimumfrequenciesofinterest;Abaqus/Standardwille*tracteigenvaluesuntileithertherequestednumberofeigenvalueshasbeene*tractedinthegivenrangeorallthefrequenciesinthegivenrangehavebeene*tracted.
See "UsingtheSIMarchitectureformodalsuperpositiondynamicanalyses〞in"Dynamicanalysisprocedures:
overview,〞 ,forinformationonusingtheSIMarchitecturewiththeLanczoseigensolver.
Input File Usage:
*FREQUENCY,EIGENSOLVER=LANCZOS
Abaqus/CAE Usage:
Stepmodule:
Step
Create:
Frequency:
Basic:
Eigensolver:
Lanczos
ChoosingablocksizefortheLanczosmethod
Ingeneral,theblocksizefortheLanczosmethodshouldbeaslargeasthelargeste*pectedmultiplicityofeigenvalues(thatis,thelargestnumberofmodeswiththesamefrequency).Ablocksizelargerthan10isnotremended.Ifthenumberofeigenvaluesrequestedis n,thedefaultblocksizeistheminimumof(7, n).Thechoiceof7forblocksizeprovestobeefficientforproblemswithrigidbodymodes.ThenumberofblockLanczosstepswithineachLanczosrunisusuallydeterminedbyAbaqus/Standardbutcanbechangedbyyou.Ingeneral,ifaparticulartypeofeigenproblemconvergesslowly,providingmoreblockLanczosstepswillreducetheanalysiscost.Ontheotherhand,ifyouknowthataparticulartypeofproblemconvergesquickly,providingfewerblockLanczosstepswillreducetheamountofin-corememoryused.Thedefaultvaluesare
Blocksize
Ma*imumnumberofblockLanczossteps
1
80
2
50
3
45
≥4
35
Automaticmulti-levelsubstructuring(AMS)eigensolver
FortheAMSmethodyouneedonlyspecifythema*imumfrequencyofinterest(theglobalfrequency),andAbaqus/Standardwille*tractallthemodesuptothisfrequency.Youcanalsospecifytheminimumfrequenciesofinterestand/orthenumberofrequestedmodes.However,specifyingthesevalueswillnotaffectthenumberofmodese*tractedbytheeigensolver;itwillaffectonlythenumberofmodesthatarestoredforoutputorforasubsequentmodalanalysis.
Thee*ecutionoftheAMSeigensolvercanbecontrolledbyspecifyingthreeparameters:
and
.Thesethreeparametersmultipliedbythema*imumfrequencyofinterestdefinethreecut-offfrequencies.
(defaultvalueof5)controlsthecutofffrequencyforsubstructureeigenproblemsinthereductionphase,while
and
(defaultvaluesof1.7and1.1,respectively)controlthecutofffrequenciesusedtodefineastartingsubspaceinthereducedeigensolutionphase.Generally,increasingthevalueof
and
improvestheaccuracyoftheresultsbutmayaffecttheperformanceoftheanalysis.
Requestingeigenvectorsatallnodes
Bydefault,theAMSeigensolverputeseigenvectorsateverynodeofthemodel.
Input File Usage:
*FREQUENCY,EIGENSOLVER=AMS
Abaqus/CAE Usage:
Stepmodule:
Step
Create:
Frequency:
Basic:
Eigensolver:
AMS
Requestingeigenvectorsonlyatspecifiednodes
Alternatively,youcanspecifyanodeset,andeigenvectorswillbeputedandstoredonlyatthenodesthatbelongtothatnodeset.Thenodesetthatyouspecifymustincludeallnodesatwhichloadsareappliedoroutputisrequestedinanysubsequentmodalanalysis(thisincludesanyrestartedanalysis).Ifelementoutputisrequestedorelement-basedloadingisapplied,thenodesattachedtotheassociatedelementsmustalsobeincludedinthisnodeset.putingeigenvectorsatonlyselectednodesimprovesperformanceandreducestheamountofstoreddata.Therefore,itisremendedthatyouusethisoptionforlargeproblems.
Input File Usage:
*FREQUENCY,EIGENSOLVER=AMS,NSET=name
Abaqus/CAE Usage:
Stepmodule:
Step
Create:
Frequency:
Basic:
Eigensolver:
AMS:
Limitregionofsavedeigenvectors
ControllingtheAMSeigensolver
TheAMSmethodconsistsofthefollowingthreephases:
Reductionphase:
InthisphaseAbaqus/Standardusesamulti-levelsubstructuringtechniquetoreducethefullsysteminawaythatallowsaveryefficienteigensolutionofthereducedsystem.Theapproachbinesasparsefactorizationbasedonamulti-levelsupernodeeliminationtreeandalocaleigensolutionateachsupernode.Startingfromthelowestlevelsupernodes,weuseaCraig-Bamptonsubstructurereductiontechniquetosuccessivelyreducethesizeofthesystemasweprogressupwardintheeliminationtree.Ateachsupernodealocaleigensolutionisobtainedbasedonfi*ingthedegreesoffreedomconnectedtothene*thigherlevelsupernode(thesearethelocalretainedor"fi*ed-interface〞degreesoffreedom).Atthe
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