Nonlinear Piezothermoelasticity and Multi-Field Actuations, Part 1: Nonlinear Anisotropic Piezothermoelastic Shell Laminates

Abstract

Nonlinear characteristics, either material or geometrical nonlinearity, and temperature variations can significantly influence the performance and reliability of piezoelectric sensors, actuators, structures, and systems. This paper is intended to examine the nonlinear piezothermoelastic characteristics and temperature effects of piezoelectric laminated systems, and it is divided into two parts. Part 1 is concerned with a mathematical modeling of nonlinear anisotropic piezothermoelastic shell laminates and Part 2 is a study of static and dynamic control of a nonlinear piezoelectric laminated circular plate subjected to mechanical, electric, and temperature excitations. Geometric nonlinearity induced by large deformations is considered in both parts. A generic nonlinear piezothermoelastic shell lamination theory is proposed and its nonlinear thermo-electromechanical equations are derived based on Hamilton’s principle. Thermo-electromechanical couplings among the elastic, electric, and temperature fields are discussed, and nonlinear components identified. Applications of the nonlinear theory to other materials, continua, sensors, actuators, and linear systems are discussed.