Free vibration of functionally graded arbitrary straight-sided quadrilateral plates in thermal environment

As a first endeavor, the free vibration of functionally graded (FG) arbitrary straight-sided quadrilateral plates under thermal environment and based on the first order shear deformation theory (FSDT) is presented. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The initial thermal stresses are evaluated by solving the thermo-elastic equilibrium equations. The solution procedure is based on transformation of the governing equations from physical domain to computational domain and then the discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. The accuracy of the present method is demonstrated by studying the free vibration of isotropic and FG plates with various shapes and comparing the solutions obtained against existing results in literature. Then, the effects of thickness-to-length ratio, volume fraction index, temperature rise, geometrical shape and the boundary conditions on the frequency parameters of the plate are studied.