THEORETIC SOLUTION FOR RECTANGULAR CANTILEVER THICK PLATES BY SYMPLECTIC GEOMETRY METHOD

A theoretic solution for rectangular cantilever thick plate is derived by symplectic geometry method.The simplified equations for elastic thick plate given by Hu are transferred into Hamilton canonical equations.The symplectic geometry method is used to separate the whole variables and the eigenvalues are obtained.With the method of eigen-function expansion,the explicit solution for rectangular cantilever thick plate is presented.Since the basic elasticity equations of thick plate is used only,the prior selection of the deformation function is rendered unnecessary.Therefore,the solution in the paper is more reasonable.A numerical example is presented to verify the present solution.