Free Vibration Analysis of Two-Dimensional Functionally Graded Annular Sector Plates with Piezoelectric Layers Resting on Two-Parameter Elastic Foundation

In this paper, free vibration analysis of two-dimensional functionally graded annular sector plates with two piezoelectric layers on elastic foundation using the Rayleigh-Ritz method is investigated applying the third order shear deformation theory of plates. Despite the existence of more complex equations, the third-order shear deformation theory of plates leads to more accurate results, this is due due to the effects of transverse shear deformation and inertial rotation,.The material properties of the annular plate is graded two-dimensionally in both of the circumferential and thickness directions. The volume fraction power law distribution is used to model the two dimensional functionally graded plate properties. The sinusoidal function is used to determine the electrical potential of the piezoelectric layers. The assumed potential function satisfies the Maxwell electrostatic equations. To obtain the natural frequencies of the plate, the Lagrangian function is defined by subtracting the kinetic and potential energies of the plate and then the Hamilton’s principle and the Ritz method is applied to obtain the natural frequencies of the plate. Finally, the results are validated by various references and the effect of various parameters including the sector angle, ratio of thickness to radius of the plate and foundation coefficients on the natural frequency of the structure has been discussed.