Zq. Cheng et Rc. Batra, Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates, J SOUND VIB, 229(4), 2000, pp. 879-895
We use Reddy's 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 un
iform in-plane hydrostatic loads. Young's modulus and the Poisson ratio for
the material of the plate are assumed to vary only in the thickness direct
ion. Effects of rotary inertia are considered, The problem of determining t
he 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 critica
l 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. (C) 2000 Academic Press.