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Chapter 4 Application of Second Order Differential Equations in mechanical Engineering AnalysisTai-Ran Hsu, ProfessorDepartment of mechanical and Aerospace EngineeringSan Jose State UniversitySan Jose, California, USAME 130 Applied Engineering AnalysisChapter Outlines Review solution method of Second Order , homogeneous ordinary Differential Equations applications in free vibration analysis- Simple mass-spring system- Damped mass-spring system Review solution method of Second Order , non-homogeneous ordinary Differential Equations - applications in forced vibration analysis- Resonant vibration analysis- Near resonant vibration analysis Modal analysis Part 1 Review Solution Method of Second Order , Homogeneous Ordinary Differential EquationsTypical form0)()()(22=++xbudxxduadxxud( )where a and b in Equation ( ) are constantsThe solution of Equation ( ) u(x) may be obtained by ASSUMING:u(x) = emx( )in which m= constantto be determinedIf the assumed solution u(x) in Equation ( ) is valid solution, it must SATISFY theDE in Equation ( ).
Chapter 4 Application of Second Order Differential Equations in Mechanical Engineering Analysis Tai-Ran Hsu, Professor Department of Mechanical …
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