LNDYN-L05-ModalTransientDynamics

ModalTransientDynamicsLecture5L5.2LinearDynamicswithAbaqusOverview•Introduction•ExcitationandOutput•Example•SubspaceSolutionsforTransientDynamics•WorkshopIntroductionL5.4LinearDynamicswithAbaqusIntroduction•Transient(time-domain)analysisbymodalsuperpositionhasspecificapplications:•Linearstructuressubjectedtotransientloading.•Structuresforwhichthedynamicresponsecanbedescribedaccuratelybyalimitednumberofthesystem’seigenmodes,includingresidualmodesifneeded.*MODALDYNAMIC,CONTINUE=(NO/YES)t_inc,t_periodt_inc=fixedsolutiontimeincrementt_period=timeperiodofthestepL5.5LinearDynamicswithAbaqusIntroduction•ThemodaldynamicprocedureinAbaqus•Analyticallyintegratesintimetheuncoupledmodalequations(reducedequationsofmotion)tosolveforthegeneralizeddisplacements(GU)oftheeigenmodes.•Recall,theeigenmodegeneralizeddisplacementsaresimplyscalingfactorsforthemodeshapes.•Theintegrationprocedureisexactiftheloadsvarypiecewiselinearlyintime.•Thestructure’snodalDOFsolutionintimeisobtainedbysummingthescaledmodeshapes.•Derivedoutput(stress,strain,sectionforces,etc.)isobtainedfromthestructure’snodalDOFsolution.L5.6LinearDynamicswithAbaqusIntroduction•ThemodaldynamicprocedureinAbaqus(cont'd)•Veryinexpensivecomparedtodirectintegrationmethods,especiallyifmultipleloadcasesareofinterest.•Theprimaryexpenseistheinitialeigenfrequencyextraction.•Theeigenmodestobeusedcanbechosenwiththe*SELECTEIGENMODESoption,whichisinputashistorydata.•If*SELECTEIGENMODESisnotused,thenalloftheextractedeigenmodeswillbeusedinthemodaldynamicanalysis.•The*SELECTEIGENMODESoptionisnotsupportbyAbaqus/CAE(usetheKeywordsEditor).L5.7LinearDynamicswithAbaqusIntroduction•ThemodaldynamicprocedureinAbaqus(cont'd)•UsestheSIMarchitectureifactivatedinthefrequencyextractionstep•Improvedperformanceandadditionaldampingoptions•Damping(traditionalarchitecture):•Global(viscousonly)•Modal•Direct(provideacriticaldampingfractionpermode).•Rayleigh(a-bdampingpermode).•Composite(criticaldampingfractionpermodebasedonmaterials).•Modalstructuraldampingfactorisnotapplicable.•Damping(SIMarchitecture):•Global(viscousandstructural)•Modal(includingstructural)•Material/elementL5.8LinearDynamicswithAbaqusIntroduction•ThemodaldynamicprocedureinAbaqus(cont'd)•Canbeperformedasarestartfromanaturalfrequencyanalysis.•Veryeffectivewhenrelativelyfewfrequenciesanddeformationmodesdominatethedynamicresponse.•Becomeslesseffectiveasthefrequencycontentoftheresponseincreases(moreeigenmodesrequired).•Notpracticalforhighfrequency(i.e.,shortwavelength)wavepropagationanalysiswherelargenumbersofeigenmodesareneededtocharacterizetheresponse.•Enablestheanalysttoinvestigatetheinfluenceofindividualmodesontheoverallstructuralresponse.L5.9LinearDynamicswithAbaqusIntroduction•Applicability•Tojudgewhethermodaldynamicscanbeusedeffectively,consider:•Canthetime-dependentloadsbedescribedaccuratelyusingtheextractedeigenmodes?•Canthemodeshapescharacterizetheloadspatialdistribution?(alsoconsidertheuseofresidualmodes,seeLecture2)•Theprocedurerequiresthatdominantloadingfrequenciesbeintherangeoftheextractedeigenfrequencies.•Cantheinitialconditionsbedescribedaccuratelyusingtheeigenmodes?•Cantheinitialaccelerationsgeneratedbysuddenlyappliedloadsbedescribedaccuratelybytheeigenmodes?•Isalinearresponseprocedureadequatetomeettheanalysisobjectives?ExcitationandOutputL5.11LinearDynamicswithAbaqusExcitationandOutput•Therearethreeformsofexcitationformodaldynamicproblems:•Concentratedand/ordistributedloads.•Initialdisplacementand/orvelocity.•Basemotion.•Loads•Aloadvectorisformulatedbasedonanyappliedconcentratedand/ordistributedloads.•Thisloadvectorisprojectedontotheselectedmodes.•Recall,foragloballoadvectorP,theequivalentmodalloadvalueformodeiis:PTiiPL5.12LinearDynamicswithAbaqusExcitationandOutput•Initialconditions•Initialdisplacementand/orvelocityconditionsmustbeprojectedontotheeigenmodesinordertoproduceinitialvaluesforthemodalgeneralizeddisplacementsandvelocities.•Defaultiszeroinitialdisplacementandvelocity.•Initialvelocitiesaredefinedwith*INITIALCONDITIONS.•Initialdisplacementsandvelocitiescanbecarriedoverfromaprecedingmodaldynamicstep.•Initialdisplacementsfromaprecedingstaticlinearperturbationstepcanalsobecarriedover.*MODALDYNAMIC,CONTINUE=YESL5.13LinearDynamicswithAbaqusExcitationandOutput•Initialconditions(cont'd)•Anexactrepresentationoftheinitialconditionscanbeobtainedonlywhenallofthemodel’seigenmodesareusedintheprojection.•Sincearelativelysmallnumberofmodesareused,initialconditionsareapproximatedbyweightingthemwiththesystemmassmatrix.•Formodeitheinitialgeneralizeddisplacementandvelocityare:11TiiinitialiTiiinitialiqmqmMuMuL5.14LinearDynamicswithAbaqusExcitationandOutput•Basemotionexcitation•Modalparticipationfactorsareusedtoconverttheaccelerationofprimarybasemotionintoequivalentmodalloadhistories.•Multiplebasemotionsarealsoallowedviathesecondarybase“bigmass”method.•Timehistoriesofthebasemotionsaredefinedwiththe*BASEMOTIONoptionandamplitudecurves.•DetailsofbasemotionexcitationwerediscussedinLecture4.L5.15LinearDynamicswithAbaqusExcitation