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TECHNICAL PAPERS

Nonlinear Active Cancellation of the Parametric Resonance in a Magnetically Levitated Body

[+] Author and Article Information
Hiroshi Yabuno

Institute of Engineering Mechanics and Systems, University of Tsukuba, Tsukuba-City 305-8573, Japane-mail: yabuno@esys.tsukuba.ac.jp

Ryo Kanda

Doctoral Program in Systems and Information Engineering, University of Tsukuba, Tsukuba-City 305-8573, Japan

Walter Lacarbonara

Dipartimento di Ingegneria Strutturale e Geotecnica, University of Rome La Sapienza, Rome 00184, Italy

Nobuharu Aoshima

Institute of Engineering Mechanics and Systems, University of Tsukuba, Tsukuba-City 305-8573, Japan

J. Dyn. Sys., Meas., Control 126(3), 433-442 (Dec 03, 2004) (10 pages) doi:10.1115/1.1789530 History: Received October 23, 2003; Online December 03, 2004
Copyright © 2004 by ASME
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References

Haxton,  R. S., and Barr,  A. D. S., 1972, “The Autoparametric Vibration Absorber,” Trans. ASME Journal of Engineering for Industry, 94, pp. 119–125.
Tuer,  K. L., Duquette,  A. P., and Golnaraghi,  M. F., 1992, “Vibration Control of a Flexible Beam Using a Rotational Internal Resonance Controller,” Journal of Sound and Vibration, 167, pp. 41–62.
Duquette,  A. P., Tuer,  K. L., and Golnaraghi,  M. F., 1992, “Vibration Control of a Flexible Beam Using a Rotational Internal Resonance Controller (Part 2: Experiment),” Journal of Sound and Vibration, 167, pp. 62–75.
Oueini,  S. S., Nayfeh,  A. H., and Golnaraghi,  M. F., 1997, “A Theoretical and Experimental Implementation of a Control Method Based on Saturation,” Nonlinear Dynamics, 13, pp. 189–202.
Cartmell,  M., and Lawson,  J., 1994, “Performance Enhancement of an Autoparametric Vibration Absorber by Means of Computer Control,” Journal of Sound and Vibration, 177(2), pp. 173–195.
Mustafa,  G., and Ertas,  A., 1995, “Dynamics and Bifurcations of a Coupled Column-Pendulum Oscillator,” Journal of Sound and Vibration, 182(3), pp. 393–413.
Yabuno, H., Murakami, T., Kawazoe, J., and Aoshima, N., 2003, “Suppression of Parametric Resonance in Cantilever Beam with a Pendulum (Effect of Static Friction at the Supporting Point of the Pendulum),” Trans. ASME Journal of Vibration and Acoustics, in press.
Yabuno,  H., Endo,  Y., and Aoshima,  N., 1999, “Stabilization of 1/3-Order Subharmonic Resonance Using an Autoparametric Vibration Absorber,” Trans. ASME Journal of Vibration and Acoustics, 121, pp. 309–315.
Lacarbonara, W., Chin, C. M., and Soper, R. R., 1999, “Nonlinear Vibration Control of Distributed-Parameter Systems: Perturbation Approach,” ASME Materials and Mechanics Conference, Blacksburg, VA, USA.
Lacarbonara,  W., Chin,  C. M., and Soper,  R. R., 2002, “Open-Loop Nonlinear Vibration Control of Shallow Arches via Perturbation Approach,” Trans. ASME Journal of Applied Mechanics, 69, pp. 325–334.
Soper,  R. R., Lacarbonara,  W., Nayfeh,  A. H., and Mook,  D. T., 1999, “Open-Loop Resonance-Cancellation Control for a Base-Excited Pendulum,” Journal of Vibration and Control, 7, pp. 1265–1279.
Yabuno,  H., Seino,  T., Yoshizawa,  M., and Tsujioka,  Y., 1989, “Dynamical Behavior of a Levitated Body with Magnetic Guides (Parametric Excitation of the Subharmonic Type Due to the Vertical Motion of Levitated Body),” JSME International Journal, 32(3), pp. 428–435.
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Figures

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Model of the magnetically levitated body with the active vibration absorber.
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Variation of the effective absorber coefficient with the nondimensional absorber frequency ωθ for various mass ratios.
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Variation of the effective range of control gains with the excitation amplitude for three absorber configurations.
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Theoretically obtained frequency-response curves of (a) uncontrolled and (b) controlled system for two excitation amplitudes (T solid (dashed) line denotes stable (unstable) steady state response).
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Block diagram of the phase-lock loop circuit.
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Experimentally obtained frequency-response curves of (a) uncontrolled and (b) controlled system for two excitation amplitudes.
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Experimentally obtained time histories: (a) uncontrolled and (b) controlled when zb1=0.95 mm,Ω/2π=8.0 Hz, and bd=0.87 Nm.
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Experimentally obtained FFT’s of the time histories of (a) uncontrolled and (b) controlled system when zb1=0.95 mm,Ω/2π=8.0 Hz, and bd=0.87 Nm.
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Expansion of the experimental time histories of the angle of the pendulum and the current in the motor shown in Fig. 8(b).
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Experimentally obtained time history of the controlled system when zb1=0.95 mm,Ω/2π=8.0 Hz, and bd=0.63 Nm.
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Experimentally obtained time histories when the excitation amplitude is changed from 1 mm to 1.3 mm from t=29 s to t=30 s,Ω/2π=8.0 Hz, and bd=0.54 Nm.
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Experimentally obtained time histories when the excitation frequency is changed from 8.0 Hz to 8.1 Hz, zb1 is 1.3 mm, Ω/2π is changed from 8.0 Hz to 8.1 Hz, and bd=0.54 Nm.
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-1Experimentally obtained time histories of the parametrically excited system with a passive autoparametric vibration absorber. (The dimension of the main system is the same as that mentioned in section 4.1. The frequency of the pendulum is tuned as near a half of the natural frequency 3.86 Hz of the main system, i.e., as 1.80 Hz. Excitation amplitude and frequency are 1.2 mm and 7.8 Hz, respectively.)

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