Exact solutions for free vibrations of orthotropic rectangulr thin plates on elastic foundation of two parameters

The close form exact solutions of free vibrations of thin orthotropic rectangular plates on the Pasternak elastic foundation or the elastic foundation with two parameters are solved by means of separation of variables method. It is noteworthy that the exact solutions for the plates with boundary conditions CCCC, SCCC and SSCC (S denotes simple support, and C denotes clamp) were considered impossible to be solved. In separation of variables method, the general formulation of the natural mode and the relationship among the two spatial eigenvalues and the temporal eigenvalue are directly obtained from the governing differential equation, and the coefficients of the exact eigenfunctions and the exact eigenvalue equations are determined on the basis of boundary conditions. The numerical results agree well with those in literature and FEM, this validates the correctness of the present method.