1Example47TitleTowerstructureunderaharmonicexcitationforceDescriptionPerformatimehistoryanalysisforasteeltowerstructuresubjectedtoalateralharmonicexcitationforce.Determinethelateraldisplacements,velocitiesandaccelerationswithrespecttotimevariables.Thesteeltowerstructureismodeledasabeamelementwithequivalentflexuralstiffness.Alumpedmassislocatedatthetopofthestructure.VerificationExample2StructuralgeometryandanalysismodelExample473ModelAnalysisType2-Dtimehistoryanalysis(X-Zplane)UnitSystemin,lbfDimensionHeightH=100inMassM=100lbf⋅sec2/in(intheXdirection)Dampingratioξ=0.0Analysistimet=0.3secTimestep∆t=0.001secElementBeamElementMaterialModulusofelasticityE=2.0×107psiSectionPropertyMomentofinertiaIyy=1666.667in4BoundaryConditionNode1;ConstrainallDOFsNode2;ConstrainDz.(DxandRyallowed)AnalysisCaseAharmonicexcitationforceisappliedatthenode2intheXdirection.P(t)=PosinωtlbfWhere,Po=1.0×105lbf,ω=30rad/secVerificationExample4ResultsEigenvalueAnalysisResultsTimeHistoryAnalysisResultsX-displacementsatthenode2Example475X-velocitiesatthenode2X-accelerationsatthenode2VerificationExample6ComparisonofResultsUnit:sec,inResultTheoreticalRef.1MIDAS/GenNaturalperiod0.200.19260.1990.1sec1.6081.5951.6070.2sec-3.187-3.163-3.186Lateraldisplacement(δx)0.3sec4.7424.6744.709ReferencePaz,Mario,“StructuralDynamics;TheoryandComputation”,3rdEdition,VanNostrandReinhold,NewYork,1991,pp.84∼87,EX.4-5,4-6.
