Modal bifurcation in a high-Tc superconducting levitation system

Abstract

This paper deals with modal bifurcation of a multi-degree-of-freedom high-Tc superconducting levitation system. As modeling of large-scale high-Tc superconducting levitation applications, where plural superconductingbulks are often used, it can be helpful to consider a system constitutingof multiple oscillators magnetically coupled with each other. This paperinvestigates nonlinear dynamics of two permanent magnets levitated above high-Tc superconducting bulks and placed between two fixed permanent magnets without contact.First, the nonlinear equations of motion of the levitated magnets were derived.Then the method of averaging was applied to them. It can be found from theobtained solutions that this nonlinear two degree-of-freedom system can have twoasymmetric modes, in addition to a symmetric mode and an antisymmetric mode bothof which also exist in the linearized system. One of the backbone curves in thefrequency response shows a modal bifurcation where the two stable asymmetric modesmentioned above appear with destabilization of the antisymmetric mode, thus leadingto modal localization. These analytical predictions have been confirmed in ournumerical analysis and experiments of free vibration and forced vibration. Theseresults, never predicted by linear analysis, can be important for application of high-Tc superconducting levitation systems.