Classical and Advanced Models for Laminated Plates with Piezoelectric Layers Actuated in Shear Mode

Abstract

We discuss the two-dimensional modelling of laminated plates with embedded piezoelectric layers actuated in shear mode. Refined approaches are necessary to capture all relevant phenomena characterizing the electro-mechanical interactions. The framework of our approach is a previously established Unified Formulation, which permits the use of Equivalent Single Layer as well as Layer-Wise descriptions in conjunction with higher-order thickness approximations. Two distinct model types are proposed: classical models based on Hamilton's principle and advanced models based on a novel partially mixed four-field formulation. Advanced models are capable of a priori fulfilling the interlaminar continuity of all transverse fluxes. In this paper, we adopt an analytical Navier-type closed-form solution method to solve the resulting system of coupled partial differential equations governing the static and the free-vibration problems. Different interlaminar conditions and electrode configurations are addressed. The proposed 2D models recover accurately the global and local response of exact 3D solutions available in literature. An assessment of various 2D models confirms the superiority of the advanced models with respect to classical ones. By virtue of their accuracy, the analytical solutions obtained from our higher-order advanced models could be employed for providing reference solutions for more general numerical approximation schemes like the FEM which are more suitable for practically relevant applications.