Exact free-vibration analysis of laminated plates with embedded piezoelectric layers

Abstract

Exact solutions are developed for predicting the coupled electromechanical vibration characteristics of simply supported laminated piezoelectric plates composed of orthorhombic layers. The three-dimensional equations of motion and the charge equation are solved using the assumptions of the linear theory of piezoelectricity. The through-thickness distributions for the displacements and electrostatic potential are functions of eight constants for each layer of the laminate. Enforcing the continuity and surface conditions results in a linear system of equations representing the behavior of the complete laminate. The determinant of this system must be zero at a resonant frequency. The natural frequencies are found numerically by first incrementally stepping through the frequency spectrum and refining the final frequencies using bisection. Representative frequencies and mode shapes are presented for a variety of lamination schemes and aspect ratios.