Analytical solution for the dynamic response of functionally graded rectangular plates resting on elastic foundation using a refined plate theory

A new refined plate theory for functionally graded material (FGM) plate is developed. Also, an analytical solution for the dynamic response of functionally graded rectangular plates resting on the Pasternak foundation under the transverse loading is investigated. By extending classical plate theory, the displacement field is assumed as the in-plane and transverse displacements consist of bending and shear components and it therefore does not need to use the shear correction factor. The material properties are assumed to vary continuously in the thickness direction according to the power-law form. The equations of motion are derived by using Hamilton’s principle. An analytical solution of simply supported FGM rectangular plates is presented by using state-space methods. The results obtained using the proposed refined plate theory are extensively compared with those obtained by the classical plate theory and finite element method. The accuracy of the new refined plate theory is demonstrated by comparing the results of chosen examples with ones predicted by other higher-order plate theories in previous studies. The effect of the power-law exponent index and the stiffness of the foundation on the behavior of the FGM plate are discussed in detail.