Static and Dynamic Analysis of Linear Piezoelectric Structures Using Higher Order Shear Deformation Theories

This paper explores the effects of shear deformation on piezoelectric materials and structures that often serve as substrate layers of multilayer composite sensors and actuators. Based on higher-order shear elastic deformation and electric potential distribution theories, a general mathematical model is derived. Governing equations and the associated boundary conditions for a piezoelectric beam are developed using a generalized Hamilton’s principle. The static and dynamic behavior of the piezoelectric structure is investigated. A bending problem in static analysis and a free vibration problem in dynamic analysis are solved. The obtained results are in very good agreement with the results of the exact two dimensional solution available in the literature.