Piezothermoelastic Behavior of a Pyroelectric Spherical Shell

An exact analysis on the piezothermoelastic behavior of a pyroelectric spherical shell with arbitrary thickness subjected to prescribed temperatures at two spherical surfaces is presented in the article. At first, three displacement functions are introduced to simplify the three-dimensional equations of equilibrium and the electrostatic charge equation of a spherically isotropic pyroelectric body. By expanding the displacement functions as well as the electric potential in terms of spherical harmonic functions, these equations are further converted to an uncoupled Euler-type, second-order ordinary differential equation and a coupled system of three such equations. A general solution to the homogeneous ordinary differential equations is derived. The piezothermoelastic analysis of a pyroelectric spherical shell is then given and numerical illustrations are presented.