Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers

In this paper, a nonlinear free vibration analysis of a thin annular functionally graded (FG) plate integrated with two uniformly distributed actuator layers made of piezoelectric (PZT4) material on the top and bottom surfaces of the annular FG plate is presented based on Kirchhoff plate theory. The material properties of the functionally graded core 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 the electric potential field along the thickness direction of piezoelectric layers is simulated by a sinusoidal function such that the Maxwell static electricity equation is satisfied. The differential equations of motion are solved analytically for various boundary conditions of the plate. The analytical solutions are derived and validated by comparing the obtained resonant frequencies of the piezoelectric coupled FG annular plate with those of an isotropic core plate. In a numerical study the emphasis is placed on investigating the effect of varying the gradient index of the FG plate on the free vibration characteristics of the structure. Also the good agreement between the results of this paper and those of the finite element (FE) analyses validated the presented approach.