关于声子晶体与高温超导体若干层状特性的理论研究
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摘要
声子晶体和高温超导材料是两类具有代表性的层状先进材料。这两种材料在实际应用中均存在众多基础理论问题亟待解决。其中,声子晶体材料的禁带效应使其在材料隔振降噪领域有着广泛的应用前景,同时也在带隙调控,层状结构稳定性等问题上面临着众多挑战；而高温超导材料在电工领域应用中的交流损耗直接关系到高温超导装置的安全稳定运行,一直受到高度重视。本学位论文分别针对声子晶体的弹性波带隙特性和高温超导体传输交流损耗进行了理论研究。
首先,提出了含有指数型功能梯度材料的功能梯度声子晶体,并系统研究了此类声子晶体的带隙特性和调控方法。功能梯度声子晶体是不同于经典声子晶体的材料宏观性质在空间上呈连续变化且具有弹性波禁带效应的结构“晶体”。根据功能梯度材料的制造工艺和材料性质梯度变化形式,设计了两类多种功能梯度声子晶体模型。应用平面波展开法计算能带结构,发现了功能梯度声子晶体中同样存在弹性波禁带效应。通过与经典声子晶体对比,得到了功能梯度材料对弹性波带隙结构的影响。通过对不同材料常数和几何常数下带隙结构的分析,获得了功能梯度声子晶体带隙结构调控方法,并发现了该材料在特定参数下会出现带隙消失现象。功能梯度声子晶体的提出减小了声子晶体原有的材料性质突变现象,同时为功能梯度材料和声子晶体的应用扩展了范围,为工程应用提供了理论基础。
其次,提出了同时考虑高温超导体各向异性和临界电流密度非均匀分布条件下的传输交流损耗的计算模型。高温超导体的层状结构特性使其具有强各向异性和临界电流密度的非均匀分布特性,这使得原有的交流损耗模型并不能很好的适用。为了能够更加准确的模拟真实工况下高温超导体的交流损耗,给出了外加直流磁场下高温超导体临界电流密度分别依照阶梯型、线性和平方型非均匀分布时,考虑各向异性条件下的传输交流损耗计算公式。通过对比发现在考虑各向异性条件下,临界电流密度阶梯型非均匀分布计算结果与实验结果有最好的吻合度,线性变化次之,但平方分布不再适用。此后,计算了不同磁场和传输电流下材料临界电流密度非均匀分布参数变化对传输交流损耗的影响,为高温超导体减小传输交流损耗提供了理论指导。
最后,提出了利用高温超导体传输交流损耗值计算临界电流密度非均匀分布形式的理论方法。将高温超导圆柱体分为多层,利用其电流饱和自外而内的特性,通过各层可承载电流幅值下的传输交流损耗值由外层至体心计算高温超导圆柱体中临界电流密度值。利用该理论方法获得了高温超导体实验中所用试件的临界电流密度依照七阶多项式形式分布的结果。该方法为高温超导体临界电流密度预测和描述提供了简单而可靠的方法。
本学位论文从材料应用基础性能研究出发,分别就功能梯度声子晶体的弹性波带隙特性和高温超导体考虑各向异性条件下的传输交流损耗进行了研究。为这两种层状先进材料的进一步应用提供了理论基础。
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.
首先,提出了含有指数型功能梯度材料的功能梯度声子晶体,并系统研究了此类声子晶体的带隙特性和调控方法。功能梯度声子晶体是不同于经典声子晶体的材料宏观性质在空间上呈连续变化且具有弹性波禁带效应的结构“晶体”。根据功能梯度材料的制造工艺和材料性质梯度变化形式,设计了两类多种功能梯度声子晶体模型。应用平面波展开法计算能带结构,发现了功能梯度声子晶体中同样存在弹性波禁带效应。通过与经典声子晶体对比,得到了功能梯度材料对弹性波带隙结构的影响。通过对不同材料常数和几何常数下带隙结构的分析,获得了功能梯度声子晶体带隙结构调控方法,并发现了该材料在特定参数下会出现带隙消失现象。功能梯度声子晶体的提出减小了声子晶体原有的材料性质突变现象,同时为功能梯度材料和声子晶体的应用扩展了范围,为工程应用提供了理论基础。
其次,提出了同时考虑高温超导体各向异性和临界电流密度非均匀分布条件下的传输交流损耗的计算模型。高温超导体的层状结构特性使其具有强各向异性和临界电流密度的非均匀分布特性,这使得原有的交流损耗模型并不能很好的适用。为了能够更加准确的模拟真实工况下高温超导体的交流损耗,给出了外加直流磁场下高温超导体临界电流密度分别依照阶梯型、线性和平方型非均匀分布时,考虑各向异性条件下的传输交流损耗计算公式。通过对比发现在考虑各向异性条件下,临界电流密度阶梯型非均匀分布计算结果与实验结果有最好的吻合度,线性变化次之,但平方分布不再适用。此后,计算了不同磁场和传输电流下材料临界电流密度非均匀分布参数变化对传输交流损耗的影响,为高温超导体减小传输交流损耗提供了理论指导。
最后,提出了利用高温超导体传输交流损耗值计算临界电流密度非均匀分布形式的理论方法。将高温超导圆柱体分为多层,利用其电流饱和自外而内的特性,通过各层可承载电流幅值下的传输交流损耗值由外层至体心计算高温超导圆柱体中临界电流密度值。利用该理论方法获得了高温超导体实验中所用试件的临界电流密度依照七阶多项式形式分布的结果。该方法为高温超导体临界电流密度预测和描述提供了简单而可靠的方法。
本学位论文从材料应用基础性能研究出发,分别就功能梯度声子晶体的弹性波带隙特性和高温超导体考虑各向异性条件下的传输交流损耗进行了研究。为这两种层状先进材料的进一步应用提供了理论基础。
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.
引文
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