Three-dimensional Green's Functions For Pyroelectric Ceramics

Fundamental solutions or Green's functions play an important role in both applied and theoretical studies on the physics of solids. They are foundations of a lot of further works. For example, fundamental solutions can be used to construct many analytical solutions of practical problems when boundary conditions are imposed. They are essential in the boundary element method as well as the study of cracks, defects and inclusions.Concerning the Green's functions and fundamental solutions studies of piezoelectric ceramics, many references only research electro-mechanical coupling behavior in isothermal case. The Green's functions and fundamental solutions for piezoelectric ceramics with considering temperature effection (this kind of ceramics is named pyroelectric ceramics) are studied rarely. This is mainly because adding thermal coupling equations breaks the fine properties of the pristine equations, which increases the troubles. However, for the smart structures and intelligent structure systems constructed with pyroelectric ceramics, their practical work environment universally is not isothermal. This makes that the thermal coupling effects of pyroelectric ceramics cannot be avoided.Against this background, as the study object of the familiar pyroelectric ceramics, the three-dimensional Green's functions are presented respectively for semi-infinite, infinite and two-phase pyroelectric ceramics which are loaded by steady point heat source, point force and point charge.Firstly, the steady general solution of pyroelectric ceramics is described. The corresponding non-dimensional general solution is also presented. For various kinds of point load in an infinite pyroelectric ceramics, their fundamental solutions can be obtained by constructing four new harmonic functions with undetermined constants. The undetermined constants of the harmonic functions can be obtained by using the compact general solution and the corresponding equilibrium and continuity conditions.Three-dimensional Green's functions for various kinds of point load on the surface and in the interior of a semi-infinite pyroelectric ceramics can be obtained by introducing four new suitable harmonic functions with undetermined constants, respectively. The undetermined constants can also be obtained by using the compact general solution and corresponding boundary, equilibrium and continuity conditions.According to the same method, the three-dimensional Green's functions for various kinds of point load in two-phase pyroelectric ceramics is presented by introducing eight new harmonic functions with undetermined constants. The undetermined constants can also be obtained by using the compact general solution and considering the corresponding boundary, continuity and equilibrium conditions.Finally, numerical results of corresponding coupled fields are given graphically by contours, including temperature increment, stress, electric displacement induction. Meanwhile the contours are analyzed, and some valuable engineering conclusions are obtained by analyzing contours.