Some Theoretical Investigation On The Layered Characteritics Of Phononic Crystals And High Temperature Superconductors

Phononic crystals and high-temperature superconductors are two kinds of typical layered advanced materials, and many problems need to be solved in the practical application. Phononic crystals with elastic band gaps have a broad application prospects. AC losses related to the safe and stable operation play an important role in high temperature superconductors. This thesis mainly aims at features and basic application performance of those advanced materials.Firstly, the band structures of functionally graded phononic crystals containing functionally graded materials varying exponentially are systematically investigated. Functionally graded phononic crystals, which are different from traditional phononic crystals, have gradually varying material properties in one or more spatial coordinates and the band gaps of elastic waves. We have designed four model FGPCs based on different primary preparation methods and FGM applications. The four models can be divided into two categories, according to the variational form of their functionally graded materials. By using plane-wave expansion, we calculate the band structures of functionally graded phononic crystals. Compared with traditional phononic crystals, the band structures of functionally graded phononic crystals are clearly changed by functionally graded materials. We also consider the influence of material composition, material properties and geometrical parameters on band gaps. Results show that different FGM properties can change the band structures remarkably. Our work can facilitate the design of vibration filters and noise insulators and provide more design freedom in engineering.Secondly, we propose the analytical formula for transport AC losses in high-temperature superconductor wire by considering critical current density of both inhomogeneous and anisotropic field dependent. The high anisotropy and the non-uniform critical current density distribution of high-temperature superconductors are caused by its layer structure characteristics. The analytical formula considered critical current density of both inhomogeneous and anisotropic field dependent for transport AC losses in high-temperature superconductor wire which usually carry AC transport current under applied magnetic field in typical application-like conditions. The angular dependence of critical current density is described by effective mass theory, and the HTS wire has inhomogeneous distribution cross-section of critical current density. Several distributions including the linear and quadratic and stepwise of a radius dependent critical-current density along a radial direction in the cross section of a round superconducting cylinder are assumed in analytical calculations. From the numerical results, we can observe that the result of stepwise distribution is agree with the exponential data, but the quadratic distribution no longer apply. Then, the influence of material parameters on normalized transport AC losses under different magnetic field and transport current is investigated. to reduce the transfer of AC loss provides a theoretical guidance for high-temperature superconductors. This analytical formula can explain the deviation of experimental transport current losses from the Norris formula and apply to calculate transport AC losses in realistic practical condition.Finally, the multi-layer model of high-temperature superconductor is proposed to calculate the non-uniform distribution of the critical current density. High-temperature superconductor cylinder is divided into multi-layer, the critical current density of each layer can be calculated from outside to inside. The critical current density distribution in the high-temperature superconductor cylinder follows the seven order polynomial. The method provides a simple and reliable method to calculate the critical current density distribution in high-temperature superconductor.This thesis studies the elastic band structures of functionally graded phononic crystals and the transport AC losses in high-temperature superconductor wire by considering critical current density of both inhomogeneous and anisotropic field dependent. After all, the results provide theoretical basis for two layered advanced material in realistic practical condition.