As techniques develop, the AMBs are more widely utilized in engineering fields than ever before. Their performance depends on the actively control strategies due to their complicated dynamical characteristics, which mainly arise from the electromagnetic forces. Those forces usually are nonlinear functions of the displacements of the rotor and the control current. An understanding of the dynamical characteristics of these structural systems is essential for the rules of their designing and controlling. Variations of a long time could be observed easier with a quicker time scale. In order to study the AMBs’ action during a very long time, we use the perturbation method to obtain the AMBs’ motion up to second-order time scale. In present work, the horizontal and vertical motions of a rotor-AMBs system with 8-pole legs and the time-varying stiffness are formulated. We use the multiple scales method to study the simultaneous resonance of a 1:2 sub-harmonic resonance and a primary parametric resonance for this system up to the second-order time scale. With numerical simulation, we focus on the nonlinear dynamics describing the system’s approximate solution with regard to the second-order time scale. It is found that the modulations of the amplitudes and phases of the rotor-AMBs system in higher time scale could be severely affected by changing some parameters in governing equations.

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