  The nonlinear formulation developed based on von Karman's assumptions is
employed to study the free vibration characteristics of functionally graded
material (FGM) plates subjected to thermal environment. Temperature field is
assumed to be a uniform distribution over the plate surface and varied in the
thickness direction. The material is assumed to be temperature dependent and
graded in the thickness direction according to the power-law distribution in
terms of volume fractions of the constituents. The effective material
properties are estimated from the volume fractions and the material properties
of the constituents using Mori-Tanaka homogenization method. The nonlinear
governing equations obtained using Lagrange's equations of motion are solved
using finite element procedure coupled with the direct iteration technique. The
variation of nonlinear frequency ratio with amplitude is highlighted
considering various parameters such as gradient index, temperature, thickness
and aspect ratios, and skew angle. For the numerical illustrations, silicon
nitride/stainless steel is considered as functionally graded material. The
results obtained here reveal that the temperature field and gradient index have
significant effect on the nonlinear vibration of the functionally graded plate.
