Transient bending analysis of a functionally graded circular plate with integrated surface piezoelectric layers

Abstract

Abstract Background Thin and piezoelectric materials are widely used as sensors or actuators in smart structures by embedding or surface-mounted them. Methods This paper report on the exact, explicit solution for the transient bending of a circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric material based on the classical plate theory (CPT). The material properties of the FG substrate plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents and the distribution of electric potential field along the thickness direction of piezoelectric layers is simulated by a quadratic function. The form of the electric potential field in the piezoelectric layer is considered such that the Maxwell static electricity equation is satisfied. The governing equations are solved for clamped and simply supported edge boundary condition of the circular plate. The solutions are expressed by elementary Bessel functions and derived via exact inverse Laplace transform. Results and Conclusions It is seen that the power index (g) and thickness of piezo-layer have significant effect on the deflection amplitude and natural frequency of piezo-FG plate.