Semi-analytical solution of a three-dimensional transient response of a functionally graded annular plate with a piezoelectric layer

In this paper, a semi-analytical solution for three-dimensional transient analysis of an annular plate with piezoelectric layers is investigated. The core is a functionally graded material with an exponential distribution. This method, which is a combination of the state space method, Laplace transform and its inversion, and the one-dimensional differential quadrature method, is used to obtain the response of three-dimensional motion equations plate and the stress-displacement relations of the state space equations obtaining an analytical solution in the direction of the thickness and by applying the differential quadrature method to the equations of state space, a semi-analytical solution of the plate is obtained. To obtain a solution in the time domain, the Laplace transform and its numerical inversion are used. Analyzing the convergence of the present method, the obtained numerical results have been compared with the results of articles and with results obtained from using finite element analysis. Various parameters were studied including boundary conditions, piezoelectric properties, voltage applied to the actuator, the ratio of core thickness to layers, the ratio of outer to inner radius, and the functionally graded material variations index.