Analytical and computational analyses for bending and vibration of laminated piezoelectric actuators and bimorphs

Abstract

This thesis presents an analytical and computational study of laminated piezoelectric actuators and bimorphs. A new two-dimensional electromechanical coupling model is developed. Based on the new model, the energy functional is derived, the solution of which is based on the principle of minimum total potential energy. This method is employed to investigate the bending and vibration behaviour of piezoelectric laminates. Although there are many approaches to the three-dimensional analysis of piezoelectric structures, they require complicated analysis. To simplify the analysis, this thesis presents an efficient two-dimensional model for the analysis of the electromechanical response of thick laminated piezoelectric actuators. The strain and kinetic energy of the vibration of these piezoelectric laminates are formulated based on the linear beam model and piezoelectric theory. A minimization procedure is carried out using the Ritz method. In this computational approach, the global displacements of the actuators are approximated by sets of linearly independent functions that are defined as shape functions. The geometric boundary conditions can also be satisfied in these shape functions through the inclusion of the basic functions. A similar approach is used to determine the electric potential across the piezoelectric material. A shape function is defined for the electric potential, and the electric boundary conditions are satisfied by the inclusion of the basic function for the electric potential. Using the principle of minimum total potential energy, a system of linear algebraic equations is derived. By solving this system of equations, the displacement and electric potential of the actuators can be obtained. A convergence study is carried out to determine the optimal number of terms required. To verify the accuracy and reliability of the numerical results, they are compared with the computational solutions obtained using the commercial finite element software ABAQUS. This approach does not require the discretisation of domains; hence, little computing effort is required. Two different configurations are considered for the analysis of laminated piezoelectric actuators. The first is a two-layered piezoelectric actuator. It is a thick elastic beam with a layer of piezoelectric material adhered to the top. The second is a three-layered piezoelectric actuator. It is similar to the two-layered actuator but has one more layer of piezoelectric material adhered to the bottom. In this analysis, the elastic core is modeled using Timoshenko beam theory, and the shear correction factor suggested by Mindlin is adopted. A comprehensive parametric study of the bending and vibration behaviour of the actuators is presented. The dimensionless frequency parameters are presented, and the effects of various geometric parameters are discussed. The method is then extended to study the behaviour of piezoelectric bimorphs. Parallel and anti-parallel configurations are considered. A comprehensive parametric study of the bending and vibration behaviour of the bimorphs is presented.

Date of Award	17 Feb 2010
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	C W LIM (Supervisor)