Nonlinear reduced order modeling of functionally graded plates subjected to random load in thermal environment

In this paper, large amplitude vibration of functionally graded material (FGM) plates subjected to combined random pressure and thermal load is studied using finite element modal reduction method. The material properties, which are depended on the temperature, vary in the thickness direction by a simple power law distribution in terms of the volume fraction of the constituents. The equations of motion in structural node degrees of freedom (DOF) are obtained based on von-Karman large deflection and first order shear deformation theory. The order of these equations is reduced using a novel approach for selection of the base vectors. Then the numerical results of the obtained reduced-order equations are compared with those of reduced-order equations obtained by other base vectors and also with those of full finite element method. It is shown that the proposed set of base vectors forms an excellent candidate for reducing the order of the equations of motion.