1Example30TitleSimplebeamwithalumpedmasssupportedontwospringsDescriptionCalculatethenaturalperiodoffreevibrationofabeamwithalumpedmass.StructuralgeometryVerificationExample2MODELAnalysisType2-Deigenvalueanalysis(X-Yplane)UnitSystemin,lbfDimensionLengthL=120inSpringconstantK=300lbf/inElementBeamelementMaterialModulusofelasticityE=30×106psiSectionPropertyMomentofinertiaIyy=1.0in2BoundaryConditionNodes1,2and3;ConstrainDxNodes1and3;Yspringconstant=300lbf/inAnalysisCaseAlumpedmass,M=1000/386lbf⋅sec2/inexistsatthenode2.Example303ResultsEigenvalueAnalysisResultsComparisonofResultsUnit:psiResultTheoreticalSTAAD/PROMIDAS/GenNaturalperiod0.5330.5330.533ReferencesTimoshenko,YoungandWeaver,“VibrationProblemsinEngineering”,4thEdition,p.11,Problem1.1-3.“STAAD-III/ISDS,GettingStartedandExampleManual”,ResearchEngineers,Inc.,1994,VerificationproblemNo.2.
