Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 18, Issue 3, Pages 755-778Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S021812740802063X
Keywords
multiple limit cycles; rotor-active magnetic bearing; Hamiltonian system; bifurcation; detection function
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The bifurcations of multiple limit cycles for a rotor-active magnetic bearings (AMB) system with the time-varying stiffness are considered in this paper. The governing nonlinear equation of motion is established for the rotor-AMB system with single-degree-of-freedom and parametric excitation. Using the method of multiple scales, the governing nonlinear equation of motion is first transformed to the averaged equation, which is in the form of a Z(2)-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, the bifurcation theory of planar dynamical system and the method of detection function are utilized to analyze the bifurcations of multiple limit cycles of the averaged equation. Four groups of parametric controlling conditions are given to obtain the configurations of compound eyes. It is found that there exist respectively at least 17, 19, 21 and 22 limit cycles in the rotor-AMB system with the time-varying stiffness under the different controlling conditions.
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