Vibrational response of functionally graded circular plate integrated with piezoelectric layers: An exact solution

In this paper, harmonic forced vibration of circular functionally graded plate integrated with two uniformly distributed actuator faces made of piezoelectric material is studied. The material properties of the functionally graded substrate layers are assumed to be graded in the thickness direction according to the power-law distribution, also the distribution of electric potential field along the thickness direction of piezoelectric layers is modeled by a quadratic function. The governing equations are solved for simply supported boundary condition of the sandwich circular plate and the solutions are presented by elementary Bessel functions. The performance of the present model is compared with that of ?nite element analyses as well as other available literature by the presentation of comparative results obtained for several examples encompassing different power indexes and vibration modes. The results show that thickness of piezoelectric layer and changing the power index in FG material has a significant influence on the deflection and natural frequencies of system.