Two-dimensional Green’s Functions For The Two-phase Material Of Fluid And Pyroelectric Ceramic

Green’s function, also called source function or influence function, is the basis of nu-merical calculation and theoretical analysis in the solid mechanics. Not only is Green’s func-tion the prerequisite in boundary element method, but also the basis of the study of cracks, defects, inclusions and contacts. Along with the progress of the time, more problems are brought with the wider application of pyroelectric ceramic in some fields like machinery, aerospace and electronic equipment. During the practice, the pyroelectric ceramic devices such as sensor, actuator and energy capture device, are required to work in the fluid usually. Due to the thermo-electro-mechanical coupling, it becomes more difficult to analyze the cou-pling and design the pyoelectric ceramic devices. In this background, this thesis conducts a systemic research aimed at the two-dimensional coupling of fluid and the pyroelectric ceramic media, obtaining the general solutions and the two-dimensional Green’s functions under the concentrated load like force, electric charge and heat.Firstly, the constitutive equations of the fluid and the transverse isotropic pyroelectric ceramic media are introduced in this thesis. In the absence of body forces, the constitutive equations are substituted into the equations of equilibrium and the heat conduction, combined with Almansi theorem, the theory of differential operator and parameter substitution. Finally, the two-dimensional steady-state general solutions under different loading conditions are de-rived.Secondly, the effects of the line force and electric loads applied in the fluid and the transverse isotropic pyroelectric ceramic media are respectively illustrated. Based on the gen-eral solutions for the fluid-solid coupled two-phase plane, harmonic functions with load ap-plied in two different media are constructed in the paper, which will be substituted into the general solutions to get every solution of all components. And then, these solutions should be satisfied to the conditions like balance equations, continuous conditions and boundary condi-tion to make sure the undetermined constants in the solutions. Before the numerical calcula-tion, all the components for coupling field under corresponding line forces and line charges are dimensionless. The contours of all components, gained from numerical calculation, are plotted and then the effect of the interface is analyzed.In the end, the line heat respectively applied in the fluid and the transverse isotropic py-roelectric ceramic media two-phase plane. Six newly constructed harmonic functions are sub-stituted into the general solutions to obtain the fundamental solutions, which should be satis-fied to the boundary condition, continuous condition and the balance equations of line heat and line forces. Then, the undetermined constants of the general solutions can be get, by which means the expression of each component is received. The contours of the temperature increment, stress component and electric displacement component are plotted. Through the analysis, some meaningful conclusions of engineering are made.