Vibration analysis of functionally graded rectangular plates resting on elastic foundation using higher-order shear and normal deformable plate theory

The free vibration of simply supported functionally graded rectangular plates resting on two-parameter elastic foundation is studied using the higher-order shear and normal deformable plate theory of Batra and Vidoli by an analytical approach. All three displacement components are expanded in the thickness direction using the Legendre polynomials. The effects of transverse shear and normal deformations are considered and the equations of motion are derived using the principle of virtual work. A power law distribution is used to explain the variation of mechanical and physical properties through the thickness of the functionally graded plate. Governing equations are then derived and the natural frequencies and the corresponding mode shapes are obtained up to the fifth-order expansion. The numerical results are given in detail and compared with the existing works. It is shown that when fifth-order expansion is used, the results of this theory for natural frequencies of thick functionally graded rectangular plates are very close to those obtained from three dimensional elasticity theory.