Prediction of Nonlinear Resonance in Superconducting Magnetic Levitation Systems (Effect of Excitation Amplitude on Prediction)

A superconducting magnetic levitation system is susceptible to the sudden onset of large amplitude oscillations due to low damping and nonlinear magnetic forces, leading to transitions from stable to unstable states. Furthermore, the eigenfrequency of the levitated body can change with variations in mass or cooling position, highlighting the critical need for accurate identification of parameter conditions that occur resonance. Numerical calculation based on modeling faces challenges in achieving high prediction accuracy because analytical representations of magnetic forces deviate from actual forces. To address these limitations, recent advancements have introduced a data-driven approach, based on bifurcation theory, for predicting resonance in nonlinear systems. This method does not require system modeling. It enables accurate resonance prediction by analyzing changes in damping and angular frequency values, which are derived from response measurements under perturbation as the system approaches a resonant state. In this study, this data-driven approach was applied to superconducting magnetic levitation systems and specifically extended to auto-parametric resonances, which involve the transfer of vibration energy between degrees of freedom. We investigated how excitation amplitude influenced the prediction accuracy of this methodology through a stability analysis of the solutions of the equations of motion, utilizing the method of multiple scales. As a result, we confirmed that increasing the excitation amplitude accelerates the decrease in the frequency component of the perturbation as the excitation frequency approaches the resonance band. Nevertheless, since the tendency for the frequency component difference of the perturbation to decrease is observed even when the excitation amplitude changes, we theoretically demonstrated that this index remains effective for resonance prediction.