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This paper presents a three-dimensional formulation for the free vibrations of thick rectangular plates with general boundary conditions and resting on elastic foundations. The general boundary conditions are imposed by means of penalty function method. The displacements of the plates are expressed by a three-dimensional cosine series and some simple polynomial functions which introduced to ensure and accelerate the convergence of the series representation. All the unknown coefficients can be obtained by using the Rayleigh–Ritz method. Comparisons of the present results with those in available literature demonstrate the accuracy and reliability of the present formulation. Furthermore, parametric investigations are presented including the effects of boundary conditions, geometrical parameters, and elastic foundation.

Three-dimensional free vibration of thick plates with general end conditions and resting on elastic foundations