The chaotic motions were shown by the vibrations of a bulk permanent magnet (PM) supported by a cylindrical high-Tc superconductor (HTSC) under external disturbance in very early experiments. There are few theoretical studies on the nonlinear behaviors of the HTSC levitation system as the complex interaction between the HTSC and PM. In this paper, we developed a numerical program to analyze the nonlinear vibrations of the levitated PM coupled with the electromagnetic force, taking into account the heat diffusion on HTSC. When the levitation system displayed chaotic oscillations by vertical excitation, the electromagnetic and thermal characteristics of the HTSC will change. The dynamic responses are shown by comparing the calculation results in which the thermal effects are taken into account and not. The numerical results display the displacements of PM, magnetic levitation forces, the acceleration, and the maximum Lyapunov exponent. The results show that the thermal effect will influence the stability of the levitation system.

中文翻译：

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具有热效应的动态高温超导悬浮系统中的混沌运动

在非常早期的实验中，由圆柱形高温超导体 (HTSC) 支撑的块状永磁体 (PM) 在外部干扰下的振动显示了混沌运动。关于HTSC悬浮系统作为HTSC和PM之间复杂相互作用的非线性行为的理论研究很少。在本文中，我们开发了一个数值程序来分析悬浮 PM 与电磁力耦合的非线性振动，同时考虑到 HTSC 上的热扩散。当悬浮系统在垂直激励下表现出混沌振荡时，HTSC 的电磁和热特性会发生变化。通过比较考虑和不考虑热效应的计算结果来显示动态响应。数值结果显示了 PM 的位移、磁悬浮力、加速度和最大李雅普诺夫指数。结果表明，热效应会影响悬浮系统的稳定性。