Effect of the ratio between the natural frequencies of a high-T_c superconducting bearing system on internal resonance

High-T_c superconducting levitation systems can achieve stable levitation without control, but they also often show complex nonlinear dynamical behavior such as internal resonance, in which different modes resonate at the same time. This paper investigates numerically and experimentally effect of the ratio between the natural frequencies of different modes on their internal resonance in a high-T_c superconducting magnetic bearing system. Numerical analyses based on the flux frozen method have been conducted. Responses in the case that the ratio of the natural frequencies is 2 to 1 are compared with those in the case that the ratios have some difference from 2 to 1. Numerical results show that the internal resonance occurs even in the cases that the ratio has some difference, though limited, from 2 to 1, and that the more the ratio differs from 2 to 1, the more the frequency range of the resonance is shifted and the narrower it is. Experiments have also been carried out. Experimental results of the internal resonance are similar to the numerical ones qualitatively.