EXACT CORRESPONDENCE BETWEEN EIGENVALUES OF MEMBRANES AND FUNCTIONALLY GRADED SIMPLY SUPPORTED POLYGONAL PLATES

We use Reddyʹs third order plate theory to study buckling and steady state vibrations of a simply supported functionally gradient isotropic polygonal plate resting on a Winkler–Pasternak elastic foundation and subjected to uniform in-plane hydrostatic loads. Youngʹs modulus and the Poisson ratio for the material of the plate are assumed to vary only in the thickness direction. Effects of rotary inertia are considered. The problem of determining the critical buckling load or the vibration frequency of the plate is found to be analogous to that of ascertaining the frequency of a membrane clamped at the edges and whose shape coincides with that of the plate. The critical buckling load and the vibration frequency are shown to be positive. Some available results for plates symmetric about the mid-plane can be retrieved from the present analysis.