Free vibrations of elastically restrained non-uniform plates

Abstract

A simple and efficient method is presented to examine the Levy-type solutions for the free vibration of elastically restrained rectangular plates, resting on a non-uniform elastic Winkler foundation under the action of constant in-plane forces. Both the thickness of the plate and stiffness of the elastic foundation are uniform along one axis and variable along the other axis. The frequency equation is derived and concisely expressed in terms of the four fundamental solutions of the governing characteristic differential equation. If the closed form fundamental solutions of the system are not available, then approximate fundamental solutions can be obtained through a numerical algorithm which is shown to be efficient, convenient and accurate. The results are compared with those in the literature. Finally, the influence of the elastically restrained boundary conditions on the natural frequencies is investigated.