Stability and multi-pulse jumping chaotic vibrations of a rotor-active magnetic bearing system with 16-pole legs under mechanical-electric-electromagnetic excitations. (English) Zbl 1476.74059
Summary: The stability and Shilnikov-type multi-pulse jumping chaotic vibrations are investigated for a nonlinear rotor-active magnetic bearing (AMB) system with the time varying stiffness and 16-pole legs under the mechanical-electric-electromagnetic excitations. The ordinary differential governing equation of motion for the rotor-AMB system is given by a two-degree-of-freedom nonlinear dynamical system including the parametric excitation, quadratic and cubic nonlinearities. The averaged equations of the rotor-AMB system are obtained by using the method of multiple scales under the cases of \(1:1\) internal resonance, primary parametric resonance and 1/2 subharmonic resonance. Some coordinate transformations are employed to find the type and number of the equilibrium points for the averaged equations. Using the global perturbation method developed by G. Kovačič and S. Wiggins [Physica D 57, No. 1–2, 185–225 (1992; Zbl 0755.35118)], the explicit sufficient conditions near the resonance are obtained for the existence of the Shilnikov-type multi-pulse jumping homoclinic orbits and chaotic vibrations. This implies that the Shilnikov-type multi-pulse jumping chaotic vibrations may occur for the rotor-AMB system in the sense of Smale horseshoes. Numerical simulations are presented to verify the analytical predictions by using the fourth-order Runge-Kutta method. The Shilnikov-type multi-pulse jumping chaotic vibrations can exist in the rotor-AMB system with the time varying stiffness and 16-pole legs under the mechanical-electric-magnetic excitations.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74H65 | Chaotic behavior of solutions to dynamical problems in solid mechanics |
| 74H55 | Stability of dynamical problems in solid mechanics |
| 74F15 | Electromagnetic effects in solid mechanics |
Keywords:
Shilnikov type chaos; Melnikov method; stability; 1:1 internal resonance; method of multiple scalesCitations:
Zbl 0755.35118References:
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