A class of rectangular moderately thick plate models was abstracted from the practical mechanics problems and solved by the symplectic system method.Firstly,the model was trans-formed into a Hamiltonian system through appropriate transformations.Then,the eigenvalues and eigenfunction systems of the Hamiltonian operator were obtained.The completeness of the eigen-function systems was verified to give a general solution for the two opposite edges simply suppor-ted.Finally,the vibration and buckling problems of Mindlin plates and rectangular moderately thick plates on Pasternak-type two-parameter elastic foundations were considered under six different boundary conditions,and the data comparisons showed the correctness of the proposed model and the effectiveness of the symplectic method.
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