Subharmonic Resonance in Magnetic Levitation of the High-Temperature Superconducting Bulks YBa2Cu3O7-x Under Harmonic Excitation

High-temperature superconducting (HTS) bulk YBa 2 Cu 3 O 7-x (YBCO) can achieve self-stable magnetic levitation (maglev) over a permanent magnet (PM) for its inherent flux pinning effect, which has considerable potential for engineering applications. The complicated vibration response, however, is lacking in research for the nonlinearity of the interaction force between the HTS bulks and PMs. This paper mainly focuses on the subharmonic resonance of the HTS bulks YBCO levitating above the PMs in Halbach array, which are in reciprocating motion, by numerical simulations. In general, the motion of HTS bulks is approximately harmonic under limited excitation. When the amplitude and frequency of the excitation satisfy certain conditions, the dynamical system undergoes a period-double bifurcation, and then, the subharmonic resonance occurs. Moreover, the period-double bifurcation brings the jump phenomenon when the frequency of excitation increases and decreases at the double of eigenfrequency nearby. Simulations show that a suitable damping is able to reduce the vibration markedly. The subharmonic resonance region in an amplitude-frequency plane is presented in this paper finally. In a word, the subharmonic resonance would occur in an HTS maglev system under certain conditions and its prediction is numerically studied here with a nonlinear mathematics model of the levitation force.