New exact solutions for free vibrations of rectangular thin plates by symplectic dual method

DOI10.1007/S10409-008-0208-4zbMath1270.74099OpenAlexW2138024150MaRDI QIDQ361970

Bo Liu, Yu-Feng Xing

Publication date: 20 August 2013

Published in: Acta Mechanica Sinica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10409-008-0208-4

zbMATH Keywords

frequencyfree vibrationsexact solutionclassical theory of thin platesymplectic dual method

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Vibrations in dynamical problems in solid mechanics (74H45) Plates (74K20)

Related Items (10)

Study on vibration characteristics in periodic plate structures using the spectral element method ⋮ A hybrid-stress element based on Hamilton principle ⋮ Closed-form solutions for free vibrations of rectangular Mindlin plates ⋮ Comprehensive exact solutions for free in-plane vibrations of orthotropic rectangular plates ⋮ New closed-form solutions for flexural vibration and eigen-buckling of nanoplates based on the nonlocal theory of elasticity ⋮ Review of solution methodologies for structural analysis of composites ⋮ High-accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain ⋮ Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation ⋮ An extended separation-of-variable method for free vibration of rectangular Mindlin plates ⋮ A symplectic eigenfunction expansion approach for free vibration solutions of rectangular Kirchhoff plates

Cites Work

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• Transversal vibrations of double-plate systems
• Theoretic solution of rectangular thin plate on foundation with four free edges by symplectic geometry method
• Hamiltonian system and symplectic geometry in mechanics of materials. III: Flexure and free vibration of plates
• Research on thick plate vibration: a literature survey
• The free vibration of rectangular plates

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