A Piezothermoelastic Thin Shell Theory Applied to Active Structures

Abstract

“Smart” structures with integrated sensors, actuators, and control electronics are of importance to the next-generation high-performance structural systems. Piezoelectric materials possess unique electromechanical properties, the direct and converse effects, which, respectively, can be used in sensor and actuator applications. In this study, piezothermoelastic characteristics of piezoelectric shell continua are studied and applications of the theory to active structures in sensing and control are discussed. A generic piezothermoelastic shell theory for thin piezoelectric shells is derived, using the linear piezoelectric theory and Kirchhoff-Love assumptions. It shows that the piezothermoelastic equations, in three principal directions, include thermal induced loads, as well as conventional electric and mechanical loads. The electric membrane forces and moments induced by the converse effect can be used to control the thermal and mechanical loads. A simplification procedure, based on the Lamé parameters and radii of curvatures, is proposed and applications of the theory to (1) a piezoelectric cylindrical shell, (2) a piezoelectric ring, and (3) a piezoelectric beam are demonstrated.