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The nonlinear vibration of high temperature superconducting (HTS) bulks in an applied permanent magnetic array (Halbach array) field, as a precondition for commercial application to HTS maglev train and HTS bearing, is systematically investigated. This article reports the actual vibration rules of HTS bulks from three aspects. First, we propose a new numerical model to simplify the calculation of levitation force. This model could provide precise simulations, especially the estimation of eigenfrequency. Second, an approximate analytic solution of the vibration of the HTS bulks is obtained by using the method of harmonic balance. Finally, to verify the results mentioned above, we measure the vertical vibration acceleration signals of an HTS maglev model, consisting of eight YBaCuO bulks, oscillating freely above a Halbach array with large displacement excitation. Higher order harmonic components, which indicate …