Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material
Ye Tang, Jiye Xu, Tianzhi Yang
Topics & Concepts
DiscretizationFunctionally graded materialFinite element methodTimoshenko beam theoryTube (container)Quadrature (astronomy)Natural frequencyMaterial propertiesHamilton's principleBeam (structure)Transverse planeStructural engineeringRitz methodEquations of motionMathematicsMechanicsMaterials scienceMathematical analysisPhysicsClassical mechanicsAcousticsEngineeringBoundary value problemComposite materialVibrationOpticsComposite Structure Analysis and OptimizationVibration and Dynamic AnalysisStructural Load-Bearing Analysis