Multiple Support Excitation.pdf

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1、MultiplesupportexcitationGiacomoBoffiDefinitionsEquationofmotionMultiplesupportexcitationEOMExampleResponseAnalysisResponseAnalysisExampleGiacomoBoffiDipartimentodiIngegneriaStrutturale,PolitecnicodiMilanoJune1,2011OutlineMultiplesupportexcitationGiacomoBoffiDefini

2、tionsEquationofmotionDefinitionsEOMExampleResponseAnalysisEquationofmotionResponseAnalysisExampleEOMExampleResponseAnalysisResponseAnalysisExampleDefinitionsMultiplesupportexcitationGiacomoBoffiDefinitionsEquationofmotionConsiderthecaseofastructurewherethesuppor

3、tsareEOMExamplesubjectedtoassigneddisplacementshistories,ui=ui(t).ResponseAnalysisTosolvethisproblem,westartwithaugmentingthedegreesResponseoffreedomwiththesupportdisplacements.AnalysisExampleWedenotethesuperstructureDOFwithxT,thesupportDOFwithxgandwehaveag

4、lobaldisplacementvectorx,xTx=.xgTheEquationofMotionMultiplesupportexcitationGiacomoBoffiDefinitionsEquationofmotionDampingeffectswillbeintroducedattheendofourEOMExamplemanipulations.ResponseAnalysisTheequationofmotionisResponseAnalysisExampleMMgx•TKKgxT0T+T

5、=MgMggx•gKgKggxgpgwhereMandKaretheusualstructuralmatrices,whileMgandMggare,inthecommoncaseofalumpedmassmodel,zeromatrices.StaticComponentsMultiplesupportexcitationGiacomoBoffiDefinitionsEquationofmotionEOMExampleWedecomposethevectorofdisplacementsintotwoRespon

6、secontributions,astaticcontributionandadynamicAnalysiscontribution,attributingthegivensupportdisplacementstoResponseAnalysisExamplethestaticcontribution.xTxsx=+xgxg0wherexistheusualrelativedisplacementsvector.DeterminationofstaticcomponentsMultiplesupportex

7、citationGiacomoBoffiBecausethexgaregiven,wecanwritetwomatricialDefinitionsequationsthatgiveusthestaticsupertructuredisplacementsEquationofandtheforceswemustapplytothesupports,motionEOMExampleKxs+Kgxg=0ResponseAnalysisKTx+Kx=pgsggggResponseAnalysisExampleFromth

8、efirstequationwehavex=-K-1Kxsggandfromthesecondwehavep=(K-KTK-1K)xggggggThesupportforcesarezerowhenthestructureisisostaticorthestructureissubjectedtoarigifmotion.DeterminationofstaticcomponentsMultiples