Exact solution for Transient bending of a circular plate integrated with piezoelectric layers

This paper presents the exact, explicit solution for the transient motion of a circular plate surface bonded by two piezoelectric layers, based on Kirchhoff plate model. The distribution of eclectic potential along the thickness direction is simulated by a quadratic function so that the Maxwell static electricity equation is satisfied. The piezoelectric layers are electrically grounded over the edge and electrodes at the two surfaces of the piezoelectric layers are shortly connected. The differential equations of motion are solved for simply supported and clamped boundary conditions. The solutions are expressed by elementary Bessel functions and obtained via exact inverse Laplace transform.