ABAQUS关于固有频率的提取方法.docx

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

 Naturalfrequencyextraction

Products:

 Abaqus/Standard  Abaqus/CAE  Abaqus/AMS  

References

∙“Procedures:

overview,〞 

∙“Generalandlinearperturbationprocedures,〞 

∙“Dynamicanalysisprocedures:

overview,〞 

∙*FREQUENCY

∙“Configuringafrequencyprocedure〞in“Configuringlinearperturbationanalysisprocedures,〞 

Overview

Thefrequencyextractionprocedure:

∙performseigenvalueextractiontocalculatethenaturalfrequenciesandthecorrespondingmodeshapesofasystem;

∙willincludeinitialstressandloadstiffnesseffectsduetopreloadsandinitialconditionsifgeometricnonlinearityisaccountedforinthebasestate,sothatsmallvibrationsofapreloadedstructurecanbemodeled;

∙willputeresidualmodesifrequested;

∙isalinearperturbationprocedure;

∙canbeperformedusingthetraditionalAbaqussoftwarearchitectureor,ifappropriate,thehigh-performanceSIMarchitecture（see “UsingtheSIMarchitectureformodalsuperpositiondynamicanalyses〞in“Dynamicanalysisprocedures:

overview,〞 ）;and

∙solvestheeigenfrequencyproblemonlyforsymmetricmassandstiffnessmatrices;theplexeigenfrequencysolvermustbeusedifunsymmetriccontributions,suchastheloadstiffness,areneeded.

 Eigenvalueextraction

Theeigenvalueproblemforthenaturalfrequenciesofanundampedfiniteelementmodelis

 where

isthemassmatrix（whichissymmetricandpositivedefinite）;

 isthestiffnessmatrix（whichincludesinitialstiffnesseffectsifthebasestateincludedtheeffectsofnonlineargeometry）;

istheeigenvector（themodeofvibration）;and

M and N

aredegreesoffreedom.

When 

 ispositivedefinite,alleigenvaluesarepositive.Rigidbodymodesandinstabilitiescause 

 tobeindefinite.Rigidbodymodesproducezeroeigenvalues.Instabilitiesproducenegativeeigenvaluesandoccurwhenyouincludeinitialstresseffects.Abaqus/Standardsolvestheeigenfrequencyproblemonlyforsymmetricmatrices.

Selectingtheeigenvalueextractionmethod

Abaqus/Standardprovidesthreeeigenvalueextractionmethods:

∙Lanczos

∙Automaticmulti-levelsubstructuring（AMS）,anadd-onanalysiscapabilityforAbaqus/Standard

∙Subspaceiteration

Inaddition,youmustconsiderthesoftwarearchitecturethatwillbeusedforthesubsequentmodalsuperpositionprocedures.Thechoiceofarchitecturehasminimalimpactonthefrequencyextractionprocedure,buttheSIMarchitecturecanoffersignificantperformanceimprovementsoverthetraditionalarchitectureforsubsequentmode-basedsteady-stateortransientdynamicprocedures（see “UsingtheSIMarchitectureformodalsuperpositiondynamicanalyses〞in“Dynamicanalysisprocedures:

overview,〞 ）.Thearchitecturethatyouuseforthefrequencyextractionprocedureisusedforallsubsequentmode-basedlineardynamicprocedures;youcannotswitcharchitecturesduringananalysis.Thesoftwarearchitecturesusedbythedifferenteigensolversareoutlinedin –1.

–1 Softwarearchitecturesavailablewithdifferenteigensolvers.

SoftwareArchitecture

Eigensolver

Lanczos

AMS

SubspaceIteration

Traditional

SIM

TheLanczossolverwiththetraditionalarchitectureisthedefaulteigenvalueextractionmethodbecauseithasthemostgeneralcapabilities.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）fileinanAMSfrequencyextractionstep.

Ifyourmodelhasmanydegreesoffreedomandtheselimitationsareacceptable,youshouldusetheAMSeigensolver.Otherwise,youshouldusetheLanczoseigensolver.TheLanczoseigensolverandthesubspaceiterationmethodaredescribedin“Eigenvalueextraction,〞 .

Lanczoseigensolver

FortheLanczosmethodyouneedtoprovidethemaximumfrequencyofinterestorthenumberofeigenvaluesrequired;Abaqus/Standardwilldetermineasuitableblocksize（althoughyoucanoverridethischoice,ifneeded）.Ifyouspecifyboththemaximumfrequencyofinterestandthenumberofeigenvaluesrequiredandtheactualnumberofeigenvaluesisunderestimated,Abaqus/Standardwillissueacorrespondingwarningmessage;theremainingeigenmodescanbefoundbyrestartingthefrequencyextraction.

Youcanalsospecifytheminimumfrequenciesofinterest;Abaqus/Standardwillextracteigenvaluesuntileithertherequestednumberofeigenvalueshasbeenextractedinthegivenrangeorallthefrequenciesinthegivenrangehavebeenextracted.

See “UsingtheSIMarchitectureformodalsuperpositiondynamicanalyses〞in“Dynamicanalysisprocedures:

overview,〞 ,forinformationonusingtheSIMarchitecturewiththeLanczoseigensolver.

Input File Usage:

*FREQUENCY,EIGENSOLVER=LANCZOS

Abaqus/CAE Usage:

Stepmodule:

 Step

Create:

 Frequency:

 Basic:

 Eigensolver:

 Lanczos

ChoosingablocksizefortheLanczosmethod

Ingeneral,theblocksizefortheLanczosmethodshouldbeaslargeasthelargestexpectedmultiplicityofeigenvalues（thatis,thelargestnumberofmodeswiththesamefrequency）.Ablocksizelargerthan10isnotremended.Ifthenumberofeigenvaluesrequestedis n,thedefaultblocksizeistheminimumof（7, n）.Thechoiceof7forblocksizeprovestobeefficientforproblemswithrigidbodymodes.ThenumberofblockLanczosstepswithineachLanczosrunisusuallydeterminedbyAbaqus/Standardbutcanbechangedbyyou.Ingeneral,ifaparticulartypeofeigenproblemconvergesslowly,providingmoreblockLanczosstepswillreducetheanalysiscost.Ontheotherhand,ifyouknowthataparticulartypeofproblemconvergesquickly,providingfewerblockLanczosstepswillreducetheamountofin-corememoryused.Thedefaultvaluesare

Blocksize

MaximumnumberofblockLanczossteps

1

80

2

50

3

45

≥4

35

Automaticmulti-levelsubstructuring（AMS）eigensolver

FortheAMSmethodyouneedonlyspecifythemaximumfrequencyofinterest（theglobalfrequency）,andAbaqus/Standardwillextractallthemodesuptothisfrequency.Youcanalsospecifytheminimumfrequenciesofinterestand/orthenumberofrequestedmodes.However,specifyingthesevalueswillnotaffectthenumberofmodesextractedbytheeigensolver;itwillaffectonlythenumberofmodesthatarestoredforoutputorforasubsequentmodalanalysis.

TheexecutionoftheAMSeigensolvercanbecontrolledbyspecifyingthreeparameters:

and 

.Thesethreeparametersmultipliedbythemaximumfrequencyofinterestdefinethreecut-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.Ateachsupernodealocaleigensolutionisobtainedbasedonfixingthedegreesoffreedomconnectedtothenexthigherlevelsupernode（thesearethelocalretainedor“fixed-interface〞degreesoffreedom）.Attheendofthereductionphasethefullsystemhasbeenreducedsuchthatth