1Example29TitleEigenvalueanalysisofatwoDOFsystemDescriptionAsimplefrictionlesstwoDOFsystemisconstructedwithtwospringsandtwolumpedmasses.Findthetwonaturalfrequenciesandthecorrespondingmodeshapes.Structuralgeometry2MODELAnalysisType2-Deigenvalueanalysis(X-Yplane)UnitSystemin,lbfDimensionLength20.0inMassM1=4.0lbf⋅sec2/inM2=1.0lbf⋅sec2/inStiffnessK=EA/LElementTrusselementMaterialModulusofelasticityE=1.0×105psiSectionPropertyAreaA=0.1in2BoundaryConditionNode3;ConstrainallDOFsNodes1and2;ConstrainDyandRz(OnlyDxallowed)AnalysisCaseMessesM1andM2existatthenodes1and2intheXdirectionrespectively.Numberofeigenvaluestobecomputed=2Example293ResultsEigenvalueAnalysisResults4ComparisonofResultsResultTheoreticalMSC/NASTRANNISAIIMIDAS/GenAngularvelocityω1(rad/sec)10.8310.8310.8310.83x11.0001.0001.0001.0001stModeEigenvaluex20.5310.5310.5310.531Angularvelocityω2(rad/sec)46.1846.1846.1846.18x1-0.133-0.133-0.133-0.1332ndModeEigenvaluex21.0001.0001.0001.000ReferencesDonaldT.Greenwood,“PrinciplesofDynamics”,EnglewoodCliff,Prentice-Hall,Inc.,1965.p.459,EX.9-1.“MSC/NASTRAN,VerificationProblemManual”,V.64,TheMacNeal-SchwendlerCorporation,1986,ProblemNo.V0301.“NISAII,VerificationManual”,Version91.0,EngineeringMechanicsResearchCorporation,1991.
