1Example33TitleEigenvalueanalysisofthecantileverDescriptionComparethenaturalfrequenciesofacantilevermodeledwithplateelementsandbeamelementsseparately.Structuralgeometryandanalysismodel2MODELAnalysisType3-DeigenvalueanalysisUnitSystemm,NDimensionLength1.0mDepth0.05mThickness0.1mGravitationalaccelerationg=1.0m/sec2ElementPlateelement(Thicktype)andbeamelementMaterialBeamElementsModulusofelasticityE=2.0×1011N/m2Poisson’sratioν=0.3Weightdensityγ=7800.0N/m3PlateElementsModulusofelasticityE=2.0×1011N/m2Poisson’sratioν=0.3Weightdensityγ=7800.0N/m3SectionPropertyBeamElementsAreaA=0.005m2EffectiveshearareaAz=4.1667×10-3m2MomentofinertiaIyy=4.166×10-6m2PlateElementsSizea×b=0.1m×0.05mThicknesst=0.1mExample603BoundaryConditionFixedend;ConstrainallDOFsTheremainingnodes;ConstrainDyandRzAnalysisCaseSelfweightisconvertedtonodalmassesautomatically.Numberofnaturalfrequenciestobecomputed=5ResultsEigenvalueAnalysisResults(Beamelements)EigenvalueAnalysisResults(Plateelements)4ComparisonofResultsUnit:HzNaturalfrequencyofthefirstmode(f1)FrequencyTheoreticalADINANISAIIMIDAS/GenPlateelements81.8081.3382.3081.87Beamelements81.8080.9481.1580.94ReferencesBlevins,R.D.,“FormulasforNaturalFrequencyandModeShape”,VanNostrandReinholdCompany,1979.“ADINA,VerificationManual-LinearProblems”,Version6.1,ADINAR&D,Inc,1992,ExampleA.47&A.66.“NISAII,VerificationManual”,Version91.0,EngineeringMechanicsResearchCorporation,1991.
