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.
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October 2006
Technical Papers
Dynamic Behavior of an AMB/Supported Rotor Subject to Parametric Excitation
Y. A. Amer,
Y. A. Amer
Department of Mathematics, Faculty of Science,
Zagazig University
, Zagazig, Egypt
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M. H. Eissa,
M. H. Eissa
Department of Engineering Mathematics,
Faculty of Electronic Engineering
, Menouf 32952, Egypt
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U. H. Hegazy,
U. H. Hegazy
Department of Mathematics, Faculty of Science,
e-mail: uhijazy@yahoo.com
Al-Azhar University
, Gaza, Palestine
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A. S. Sabbah
A. S. Sabbah
Department of Mathematics, Faculty of Science,
Zagazig University
, Zagazig, Egypt
Search for other works by this author on:
Y. A. Amer
Department of Mathematics, Faculty of Science,
Zagazig University
, Zagazig, Egypt
M. H. Eissa
Department of Engineering Mathematics,
Faculty of Electronic Engineering
, Menouf 32952, Egypt
U. H. Hegazy
Department of Mathematics, Faculty of Science,
Al-Azhar University
, Gaza, Palestinee-mail: uhijazy@yahoo.com
A. S. Sabbah
Department of Mathematics, Faculty of Science,
Zagazig University
, Zagazig, EgyptJ. Vib. Acoust. Oct 2006, 128(5): 646-652 (7 pages)
Published Online: February 14, 2006
Article history
Received:
April 1, 2005
Revised:
February 14, 2006
Citation
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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