The dynamical behavior of a parametrically excited simple rigid disk-rotor supported by active magnetic bearings (AMB) is investigated, without gyroscopic effects. The principal parametric resonance case is considered and studied. The motion of the rotor is modeled by a coupled second-order nonlinear ordinary differential equations. Their approximate solutions are sought applying the method of multiple scales. A reduced system of four first-order ordinary differential equations are determined to describe the time variation of the amplitudes and phases of the vibration in the horizontal and vertical directions. The steady-state response and the stability of the solutions for various parameters are studied numerically, using the frequency response function method. The numerical results show that the system behavior includes multiple solutions, jump phenomenon, and sensitive dependence on initial conditions. It is also shown that the system parameters have different effects on the nonlinear response of the rotor. Results are compared to previously published work.
Dynamic Behavior of an AMB/Supported Rotor Subject to Parametric Excitation
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Amer, Y. A., Eissa, M. H., Hegazy, U. H., and Sabbah, A. S. (February 14, 2006). "Dynamic Behavior of an AMB/Supported Rotor Subject to Parametric Excitation." ASME. J. Vib. Acoust. October 2006; 128(5): 646–652. https://doi.org/10.1115/1.2202163
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