Vibrations of Clamped Rectangular Plates on Elastic Foundations Subjected to Uniform Compressive Forces

This paper deals with a different solution technique for free vibrations of rectangular plates resting on elastic foundations with clamped boundaries and subjected to uniform and constant compressive, unidirectional forces in the midplane. The applied method is based on the use of a nonorthogonal series expansion consisting of some specially chosen trigonometric functions for the deflection surface $\overline{\mathit{W}}$ of the plate. The orthogonalization of the series and other calculations are performed using Fourier expansion of Bernoulli polynomials under some realistic approximations for the limiting values of the boundary conditions. In this method one need not use the solution of the differential equation of the problem. The results obtained for the problem are consistent with the well-known solutions.