Free vibration of functionally graded sandwich plates based on nth-order shear deformation theory via differential quadrature method

The present study is concerned with free vibration of functionally graded sandwich plates on elastic foundation based on nth-order shear deformation theory. The material properties of functionally graded plate are assumed to vary according to power law distribution of the volume fraction of the constituents, and two common types of FG sandwich plates are considered. Governing differential equations are derived by means of Hamilton's principle. The differential quadrature method is developed to formulate the problem, and rapid convergence is observed in this study. A numerical comparison is carried out to show the validity of the proposed theory with available results in the literature. Furthermore, effects of gradient indexes, thickness side ratio, aspect ratio, foundation parameters, boundary condition and different sandwich types on the natural frequency of plates are also studied.