Resonance behavior of a rotor-active magnetic bearing with time-varying stiffness

Chaos, Solitons and Fractals

Volumn 34, Issue 4, 2007, Pages 1328-1345

  Amer, Y A ^a   Hegazy, U H ^b  

^a Zagazig University   (Egypt)

^b AL AZHAR UNIVERSITY   (Palestine)

Author keywords

[No Author keywords available]

Indexed keywords

ORDINARY DIFFERENTIAL EQUATIONS; RESONANCE; ROTORS; STIFFNESS; SYSTEM STABILITY; VIBRATIONS (MECHANICAL);

ACTIVE MAGNETIC BEARINGS (AMB); CHAOTIC MOTION; FREQUENCY RESPONSE FUNCTION; STEADY-STATE RESPONSE; SYSTEM PARAMETERS;

MAGNETIC BEARINGS;

EID: 34247111282     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.04.040     Document Type: Article

References (27)

1. El Naschie M.S. Stress stability and chaos in structural engineering: an energy approach (1992), McGraw-Hill international editions
2. Kahraman A., and Blankenship G.W. Interactions between commensurate parametric and forcing excitations in a system with clearance. J Sound Vibr 194 (1996) 317-336
3. Kahraman A., and Blankenship G.W. Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters. J Appl Mech 64 (1997) 217-226
4. Padmanabhan C, Singh R. Influence of a mean load on the response of a forced nonlinear Hill's oscillator. ASME Design Engineering, Technical Conf., Boston, MA, 1995.
5. Nayfeh A.H., and Mook D.T. Nonlinear oscillations (1995), Wiley-Interscience, New York
6. Zhang W., and Ye M. Local and global bifurcations of valve mechanism. Nonlinear Dyn 6 (1994) 301-316
7. Ma O., and Kahraman A. Period-one motions of a mechanical oscillator with periodically time-varying, piecewise-nonlinear stiffness. J Sound Vibr 284 (2005) 893-914
8. Walsh P.L., and Lamancusa J.S. A variable stiffness vibration absorber for minimization of transient vibrations. J Sound Vibr 152 2 (1992) 195-211
9. Ji J.C., and Hansen C.H. Approximate solutions and chaotic motions of a piecewise nonlinear-linear oscillator. Chaos, Solitons & Fractals 20 (2004) 1121-1133
10. Zhang W., and Zu J.W. Nonlinear dynamic analysis for a rotor-active magnetic bearing system with time-varying stiffness. Part I: Formulation and local bifurcation. Proceedings of 2003 ASME international mechanical engineering congress and exposition, Washington (DC), November 16-21 (2003), ASME, New York 631-640
11. Zhang W., Yao M.H., and Zhan X.P. Multi-pulse chaotic motions of a rotor-active magnetic bearing system with time-varying stiffness. Chaos, Solitons & Fractals 27 (2005) 175-186
12. Zhang W., and Zhan X.P. Periodic and chaotic motions of a rotor-active magnetic bearing with quadratic and cubic terms and time-varying stiffness. Nonlinear Dyn 41 (2005) 331-359
13. Inayat-Hussain J. Chaos via torus breakdown in the vibration response of a rigid rotor supported by active magnetic bearings. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.10.039.
14. Hu T., Lin Z., Jiang W., and Allaire P.E. Constrained control design for magnetic bearing systems. ASME J Dyn Syst Meas Control 127 (2005) 601-616
15. Wang H.B., and Liu J.Q. Stability and bifurcation analysis in a magnetic bearing system with time delays. Chaos, Solitons & Fractals 26 (2005) 813-825
16. Wang H.B., and Liu J.Q. multiple stability analysis in a magnetic bearing system with time delays. Chaos, Solitons & Fractals 27 (2005) 789-799
17. Zeng S. Modeling and experimental study of the transient response of an AMB rotor during rotor drop on back-up bearings. Proceedings of the institution of mechanical engineers. Part I: J Syst Control Eng 217 (2003) 505-517
18. Wang X., and Noah S. Nonlinear dynamics of a magnetically supported rotor on safety auxiliary bearing. ASME J Vibr Acoust 120 (1998) 596-606
19. Sivrioglu S., and Nonami K. Sliding mode control with time-varying hyperlane for AMB systems. IEEE/ASME Trans Mech 3 1 (1998) 51-59
20. Jang M.J., and Chen C.K. Bifurcation analysis in flexible rotor supported by active magnetic bearing. Int J Bifurcart Chaos 11 8 (2001) 2163-2178
21. Jang M.J., Chen C.L., and Tsao M. Sliding mode control for active magnetic bearing system with flexible rotor. J Franklin Inst 342 (2005) 401-419
22. Chinta M., and Palazzolo A.B. Stability and bifurcation of rotor motion in a magnetic bearing. J Sound Vibr 214 (1998) 793-803
23. Ji J.C., Yu L., and Leung A.Y.T. Bifurcation behavior of a rotor supported by active magnetic bearings. J Sound Vibr 235 (2000) 133-151
24. Ji J.C., and Hansen C.H. Non-linear oscillations of a rotor in active magnetic bearings. J Sound Vibr 240 (2001) 599-612
25. Ji J.C., and Leung A.Y.T. Non-linear oscillations of a rotor-magnetic bearing system under superharmonic resonance conditions. Int J Non-linear Mech 38 (2003) 829-835
26. Amer YA, Eissa MH, Hegazy UH, Sabbah AS. Dynamic behavior of an AMB/supported rotor subject to parametric excitation. ASME J Vibr Acoust, in press.
27. Eissa MH, Hegazy UH, Amer YA. Dynamic behavior of an AMB supported rotor subject to harmonic excitation, submitted for publication.