Free Vibration Analysis of Thick Functionally Graded Piezoelectric Rectangular Plates in Closed Circuit Condition

In this article, free vibration analysis of thick functionally graded piezoelectric rectangular plates in closed circuit condition is investigated. Based on the higher-order shear and normal deformable plate theory, the governing equations are obtained using the principle of virtual work. The equations are then solved analytically, assuming the simply support boundary condition along all edges. In higher-order shear and normal deformable plate theory, the effects of the both transverse shear and normal deformations are considered and displacement, potentioal components are expanded in the thickness direction using the Legendre polynomials. Advantages of this theory compared to the shear theories is that given that deflection of the plate along the thickness is not constant, for thick plate provides more accurate results. A power law distribution is used to explain the variation of mechanical, electrical and physical properties through the thickness of the functionally graded materials. Furthermore, after showing the accuracy of present analytical approach, the numerical results for different parameters such as power of functionally graded piezoelectric material, various thickness to length ratio and piezoelectric effect on the plate natural frequencies has been studied.