Using two-parameter foundation model and 8-node isoparametric element based on Mindlin plate theory

the FEM equation for dynamic response analysis of elastic plates resting on elastic foundation is derived by Hamilton variation principle. The effects of foundation and mass distributed within the plate are combined in the stiffness matrix and mass matrix of the plate

and the effect of the foundation outside the plate domain is taken into account by the boundary element method. The free vibration and forced vibration of a free edge square plate are analyzed. The calculated inherent frequencies are close to measured results. Forced vibration dynamic responses reach the maximum when resonance occurs. The dynamic responses of the plate with the given damp ratio tend to be the same as those with zero damp ratio during the steady vibration period. The damp can significantly decrease the resonant responses.