1Example34TitleEigenvalueanalysisofacantileverplateDescriptionCalculatethenaturalfrequenciesofasquarecantileverplate.2StructuralgeometryandanalysismodelExample343ModelAnalysisType3-DeigenvalueanalysisUnitSystemin,kipDimensionLength24.0inWidth24.0inThickness1.0inGravitationalaccelerationg=386.4in/sec2ElementPlateelement(Thicktype)MaterialModulusofelasticityE=29.5×103ksiPoisson’sratioν=0.3Weightdensityγ=2.835648×10-4kips/in3ElementPropertyElementsizea×b=24.0/19in×24.0/19inThicknesst=1.0inBoundaryConditionNodes1~20;ConstrainallDOFs.Allnodes;ConstrainDx,DyandRz.AnalysisCaseSelfweightisconvertedtonodalmassesautomatically.Numberofnaturalfrequenciestobecomputed=54ResultsEigenvalueAnalysisResultsExample345(a)Finiteelementmodel(b)1stmode(c)2ndmode(d)3rdmode(e)4thmode(f)5thmodeFiniteelementmodelandthevibrationmodes6ComparisonofResultsUnit:secNaturalPeriodModeTheoreticalSAP2000MIDAS/Gen1st0.017900.017810.017242nd0.007320.006480.007103rd0.002920.002850.002844th0.002280.002230.002235th0.002010.001870.00197ReferencesHarris,C.M.andCrede,C.E.,“ShockandVibrationHandbook”,McGraw-Hill,1976.“SAP90,ASeriesofComputerProgramsfortheFiniteElementAnalysisofStructures,StructuralAnalysisVerificationManual”,ComputerandStructures,Inc.,1992,Example15.
