A nonlinear analysis of piezoelectric coated laminae

Abstract

In relation to vibrations of piezoelectric materials subject to strong electric fields and large strains, a system of 2-D nonlinear laminae equations is derived by the use of Mindlins kinematic hypothesis for each layer. The laminae is coated completely with perfectly conducting electrodes on both its faces, and it may comprise any number of bonded layers, each with a distinct but uniform thickness and electromechanical properties. By use of a recent variational principle [Altay and Dokmeci, Thin Walled Struct. 39, 95–109 (2001)], the system of equations is consistently formulated in both invariant, differential and variational forms. The effects of elastic stiffnesses of, and the interactions between, layers of laminae are all taken into account. The system of equations governs the extensional, flexural, and thickness shear as well as coupled vibrations of piezoelectric laminae. Special types of vibrations, geometry, and material properties are recorded. Besides, the uniqueness is investigated in solutions of the initial-mixed boundary value problems defined by the linearized system of laminae equations. [Work supported in part by TUBA.]