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Type: Journal article
Title: Hopf bifurcation of a magnetic bearing system with time delay
Author: Ji, J.
Hansen, C.
Citation: Journal of Vibration and Acoustics: Transactions of the ASME, 2005; 127(4):362-369
Publisher: ASME-Amer Soc Mechanical Eng
Issue Date: 2005
ISSN: 1048-9002
Statement of
J. C. Ji and Colin H. Hansen
Abstract: This paper is concerned with a study of the influence of a time delay occurring in a PD feedback control on the dynamic stability of a rotor suspended by magnetic bearings. In the presence of geometric coordinate coupling and time delay, the equations of motion governing the response of the rotor are a set of two-degree-of-freedom nonlinear differential equations with time delay coupling in nonlinear terms. It is found that as the time delay increases beyond a critical value, the equilibrium position of the rotor motion becomes unstable and may bifurcate into two qualitatively different kinds of periodic motion. The resultant Hopf bifurcation is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. Based on the reduction of the infinite dimensional problem to the flow on a four-dimensional center manifold, the bifurcating periodic solutions are investigated using a perturbation method.
DOI: 10.1115/1.1924644
Appears in Collections:Aurora harvest 6
Environment Institute publications
Mechanical Engineering publications

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