LNDYN-L04-BaseMotionExcitation

BaseMotionExcitationLecture4L4.2LinearDynamicswithAbaqusOverview•Introduction•PrimaryBaseMotion•SecondaryBaseMotions•Usage•ExampleIntroductionL4.4LinearDynamicswithAbaqusIntroduction•Therearemanyproblemsindynamicswhereenforcedmotionistheprimarysourceofexcitation.•Examplesincludevehiclesuspensionsrespondingtoroadirregularitiesandcivilstructuressubjectedtoseismicgroundmotions.•Theforcingfunctionsaregivenbythetimehistoryofmotionsatthesupportsofthestructure.Suchmotionsmayormaynotbeharmonicinnatureandmayormaynotbeidenticalattheindividualsupports.flatroad(reference)ufront(t)urear(t)bumpyroadL4.5LinearDynamicswithAbaqusIntroduction•Fordirectsolutionstotheequationsofmotion,theseforcingfunctionscanbeprescribedbyapplyingboundaryconditionstothenodalDOFsatsupportlocationsusing•appropriateamplitudecurvesand/or•usersubroutineDISP.•Directsolutionsareavailablefor:•Transientnonlineardynamics(implicitorexplicittimeintegration)•Steady-statedynamics(inthefrequencydomain)L4.6LinearDynamicswithAbaqusIntroduction•Formodallineardynamicprocedures,thesupportmotionsaresimulatedbyprescribingbasemotionexcitations.•A“base”isrepresentedbyDOFsthathaveprescribedboundaryconditionsintheprecedingfrequencyextraction.•The“basemotion”inputdefineshow“bases”aredriventorepresentthesupportmotions.•Multiplebasesarerequiredwhenasinglemotionisnotbeingappliedtoallofthestructure’ssupportlocations.•Forexample,abridgewhosesupportsaresubjectedtothesameearthquakerecordsbutwithatimeshift.•Theprecedingexampleofavehiclesuspension.•Basemotionexcitationisnotavailableforsubspaceprojectiontransientanalysis.L4.7LinearDynamicswithAbaqusIntroduction•Twotypesofbasedefinitionsareavailable:•PrimaryBase:•ConsistsofDOFsthatrepresentamodel’sglobalsupport.•The*BOUNDARYoptionwithouttheBASENAMEparametercorrespondstotheconstrainedprimarybaseDOFs.•Ifthesameexcitationmotionisidenticalatallsupportlocations,thenthe*BOUNDARYoptionisusedwithouttheBASENAMEparameterandallconstrainedDOFsbelongtotheprimarybase.•SecondaryBase:•Requiredifmorethanonebasemotionexcitationisprescribed.•DrivennodalDOFsaregroupedintonamedsecondarybasesviatheBASENAMEparameter(*BOUNDARY,BASENAME=...).•Morethanonesecondarybasecanbedefined.L4.8LinearDynamicswithAbaqusIntroduction•Abaqususesdifferentapproachestohandleprimaryandsecondarybasemotions.•TheModalParticipation(inertialforce)Methodisusedforprimarybasemotions.•The“bigmass”methodisusedforsecondarybasemotions.PrimaryBaseMotionL4.10LinearDynamicswithAbaqusPrimaryBaseMotion•Insomeproblemsastructureisloadedbyrigidbodymotionsofitsfoundation.•Animportantexampleisearthquakeexcitation.•Insuchproblems,weareprimarilyconcernedwithmotionsofthestructurerelativetotheidealrigidbodymotionofthestructurethatwouldoccurasaresultofthefoundation(i.e.,base)motion.•Itismotionrelativetothestructure’srigidbodyresponseduetothebasemotionthatcancausedamage(strain/stress).•Thetotalresponse,ut,ofthesystemconsistsoftherelativeresponse,u,addedtoanidealizedrigidbodyresponsethatwouldresultfromthebasemotionexcitation,ubwithsimilarexpressionsforvelocitiesandaccelerations.tbuuuL4.11LinearDynamicswithAbaqusPrimaryBaseMotion•Substitutingtheprecedingexpressionforandutintotheequationofmotion,andsettingtheexternalforcestozerogives:•Note:ubrepresentsarigidbodymotionoftheentirestructureduetothefoundationmotion.Therefore,•Assumethereisnodampingassociatedwitharigidbodymotionoftheentirestructureduetothefoundationmotion.Thiscanbeviewedastherebeingnodashpotstoanidealized“ground”thatexistsindependentoftheprimarybase.Thisimplies:tt,uu{}{}{}bbb0MuuCuuKuub0Kub0CuL4.12LinearDynamicswithAbaqusPrimaryBaseMotion•Theequationsofmotioncanthenberewrittenas:•ThesolutionDOFsarenowtherelativeresponsevariablesu,andnotthetotalresponsevariablesut.•Thefoundation(primarybase)accelerationisconvertedintoarigidbodyaccelerationvectorforthestructure.•Thestructure’srigidbodyaccelerationvectorisusedtogenerateasetofinertialoadsthatactontheunconstraineduDOFs.•TheinertialoadsaretransformedintothemodalsubspaceviatheeigenvectorParticipationFactors(ModalParticipationMethod).•Fordirectsolutionandsubspaceprojectionanalyses,basemotionscansometimesbereplacedwithdistributedinertialloadssimilartogravitationalloading.bMuCuKuMubuL4.13LinearDynamicswithAbaqusPrimaryBaseMotion•Modalparticipationmethod•Withmodalsuperpositionsolutions,theequationsofmotionareprojectedontoasubspaceofselectedmodeshapes(Lecture3).•Theinertialloadvectorassociatedwithmotionoftheprimarybaseistransformedintoanequivalentmodalloadvector.•Theprimarybasemotionsarerepresentedasavectorsumofglobaltranslationalandrotationalaccelerations.•Therefore,theequivalentmodalloadvectorcanbequicklyobtainedfromtheparticipationfactorandgeneralizedmodalmassdataoutputfromtheeigenvalueextraction.L4.14LinearDynamicswithAbaqusPrimaryBaseMotion•Modalparticipationmethod:Interface•The*BASEMOTIONoptiondefinestheexcitationoftheprimarybase(foundation).•Itisonlyavailablewithlinearperturbationmodalsuperpositionanalyses,wheretheequationsofmotionaretransformedviatheeigenfrequenciesa