On the time-response of square plates on unilateral support

Abstract

Abstract Transient response and vibrations of an elastic thin plate supported on a unilateral foundation are presented. The displacement function of the plate is approximated by using the eigenfunctions of the completely free beam. In the application of the Galerkin method the boundary conditions which cannot be satisfied by the beam functions at the corners of the plate and the edges are compensated by suitable additions to the governing equation. Although the procedure can readily be used to solve problems of plates under the action of any arbitrary loads, the problem solved numerically involves a single concentrated force. Numerical results are presented in figures to clarify the dynamic behaviour of the plate.