Study On The Interface Effects Based On Three-dimensional Green’s Functions For The Two-phase Material Of Fluid And Pyroelectric Ceramic

Green’s functions play an important role in both applied and theoretical studies on the physics of solids, which are commonly used in mathematical physical equation. They are the basement of a lot of further works including the numerical calculation such as the boundary element method and the theoretical analysis. By using the principle of superposition, they can be used to solve the engineering problems under arbitrary loads. Additionally, They are essential in the studies of cracks, defects and inclusions.Functional materials, with rapid development in recent years, are often bonded with other materials in engineering. This can result to the couple of multi-physical fields and interface effects. For the security and reliability, it is necessary to pay for the effort on the analysis and evaluation of coupling field. Fluid-structure interaction and interface problems are important parts of these engineering problems. In this thesis, we study the coupling behaviors of thermo-electro-mechanics based on the transversely isotropic pyroelectric ceramic in the fluid-structure two-phase material by using Green’s functions method. For these smart structures and intelligent structure systems which are constructed by pyroelectric ceramics, their work environment is not isothermal, hence the thermal coupling effects cannot be avoided. For understanding of the mechanism of the interaction of multi-physical fields, the coupling behaviors of the force-electricity coupling characteristics are also investigated in this thesis.For the completeness, the constitutive equations, equilibrium equations and heat conduction equation of transverse isotropic pyroelectric ceramic material are introduced firstly. With using the differential operator theory, Almansi theory and some mathematical transformations, a compact three-dimensional general solution is derived. For homogeneous dielectric fluid, the general solutions of potential and temperature increment are expressed with harmonic function. These general solutions are the foundation for the work of this thesis.The three-dimensional Green’s functions for a steady-state point heat source, a point charge source or a point force source in the interior of a fluid and pyroelectric two-phase material are presented. By virtue of the three-dimensional general solutions which are expressed in harmonic functions, some newly introduced harmonic functions with undetermined constants are constructed. Then, all the pyroelectric components in the fluid and pyroelectric two-phase material can be derived by substituting these harmonic functions into the corresponding general solutions. And the undetermined constants can be obtained by the interface compatibility conditions and the mechanical, electric and thermal equilibrium conditions. The extended Mindlin solution and the Lorentz solution are considered. Numerical results are given graphically by contours, and some valuable conclusions for engineering are presented, which can be used in the design of energy harvest device and the sensor. It is worth to point out that, since the general solutions and harmonic functions constructed in this paper is in compact form and all the components in the field are present explicitly, it is convenient to further use in both engineering and theory research.