Abstract
A discrete method is developed for analyzing the free vibration problem of square plates resting on non-homogeneous elastic foundations. The fundamental differential equations are established for the bending problem of the plate on elastic foundations. The Green function, which is obtained by transforming these differential equations into integral equations and using numerical integration, is used to get the characteristic equation of the free vibration. The effects of the modulus of the foundation and the stepped thickness on the frequency parameters are considered. By comparing the present numerical results with those previously published, the efficiency and accuracy of the present method are investigated.
