Two-Dimensional Solution of Piezoelectric Plate Subjected to Arbitrary Boundary Conditions using Extended Kantorovich Method

This paper presents a closed-form analytical method to analyze the rectangular piezoelectric plate with arbitrary boundary condition at all edges. A mixed formulation is used to formulate the governing equation. Using the basic equation of equilibrium and plate constitutive relation, a set of 16 + 3n(phi) equation are formulated in the weak form. Two sets of ordinary differential equations are obtained using the extended Kantorovich method. A single-term (n = 1) EKM solution yields reasonably good results. In this study, the numerical results are presented using the single-term solution and its convergence is achieved in two iterations. The EKM solution is computationally efficient not only for levy-type boundary condition plate but also show excellent accuracy for the arbitrary boundary conditions. As the span-to-thickness ratio increases, the percentage error value decreases. (C) 2017 The Authors. Published by Elsevier Ltd.