free vibration analysis of thick functionally graded rectangular plates using variable refined plate theory

in this paper, free vibration of functionally graded rectangular simply supported thick plates based on two variable refined plate theory is presented. according to a power-law distribution, the mass density and elasticity modulus of the plate are considered to vary while poisson’s ratio is constant. in order to extract the five constitutive equations of motion, hamilton principle is employed. the high accuracy of this theory is investigated by comparing with exact results reported by higher order shear deformation theory. furthermore, parametric study of non-dimensional natural frequencies is carried out and the influences of geometrical parameters such as aspect ratios of the plate on these frequencies are studied.