Superconducting levitation systems have been considered as a promising technology for implementing high-speed transport systems. A superconducting levitation system can levitate a magnet without active feedback control. However, due to the system's low damping and nonlinearity, large-amplitude nonlinear vibration can easily occur. Although an electromagnetic shunt damper can suppress the vibration without contact by transforming the vibrational kinetic energy into electrical energy, the inductance value of the damper often becomes too large to realize practically. Therefore, we propose a new type of electromagnetic shunt damper that is nonlinearly coupled with the levitated body, and its value of inductance can be reduced to one-fourth the conventional one. First, we evaluate the levitation force via the advanced mirror image method. Next, we perform numerical calculation via the Runge-Kutta method and nonlinear analysis via the method of multiple scales. We obtain the system's frequency responses via both these methods. From the results, we observe that internal resonance can occur and the proposed electromagnetic shunt damper can reduce the vibration amplitude.
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