Three-dimensional elastodynamic solution for an arbitrary thick FGM rectangular plate resting on a two parameter viscoelastic foundation

Abstract

A three-dimensional semi-analytic analysis based on the linear elasticity theory is offered to study the transient vibration characteristics of an arbitrarily thick, simply supported, functionally graded (FGM) rectangular plate, resting on a linear Winkler–Pasternak viscoelastic foundation, and subjected to general distributed driving forces of arbitrary temporal and spatial variations. The problem solution is obtained by adopting a laminate model in conjunction with the powerful state space solution technique involving a global transfer matrix and Durbin’s numerical Laplace inversion algorithm. Numerical calculations are carried out for the transient displacement and stress responses of aluminum-zirconia FGM square plates of selected thickness parameters and compositional gradients, resting on “soft” or “stiff” elastic foundations, under the action of moving transverse forces as well as uniformly distributed blast loads. Also, the response curves for the FGM plates are compared with those of equivalent bilaminate plates containing comparable total volume fractions of constituent materials. It is observed that the material gradient variation is substantially more influential on the dynamic stress concentrations induced across the plate thickness than on the displacement response of the inhomogeneous plates. In particular, the displacement response of the equivalent bilaminate plates can provide an accurate estimate for prediction of the dynamic response of the corresponding FGM plates, especially for thick plates resting on a stiff foundation. Limiting cases are considered and good agreements with the data available in the literature as well as with the computations made by using a commercial finite element package are obtained.