The purpose of this paper is to study the dynamics of an electromechanical system consisting of a torsion-bar or two mechanical pumps activated by an electromotor. Oscillatory solutions showing the jump and hysteresis phenomena are obtained using the harmonic balance method and direct numerical simulation. Chaotic behavior is presented via the bifurcation diagrams and corresponding Lyapunov exponent. Some implications of the results on the applications of the devices are discussed.
References
1.
Chang
, S.-C.
, and Tung
, P.-C.
, 1998, “Identification of a Nonlinear Electromagnetic System: An Experimental Study
,” J. Sound Vibr.
, 214
(5
), pp. 853
–871
.2.
Chang
, S.-C.
, and Lin
, H.-P.
, 2005, “Nonlinear Dynamics and Chaos Control for an Electromagnetic System
,” J. Sound Vibr.
, 279
, pp. 327
–344
.3.
Ji
, J. C.
, and Hansen
, C. H.
, 2005, “Hopf Bifurcation of Magnetic Bearing System With Time Delay
,” J. Vib. Acoust.
, 127
, pp. 362
–369
.4.
Belato
, D.
, Weber
, H. I.
, Balthazar
, J. M.
, and Mook
D. T.
, 2001, “Chaotic Vibrations of Nonideal Electromechanical System
,” Int. J. Solids and Struct.
, 38
, pp. 1699
–1706
.5.
Wang
, Z.
, and Chau
, K. T.
, 2008, “Anti-Control of Chaos of a Permanent Magnet DC Motor System for Vibratory Compactors
,” Chaos, Solitons Fractals
, 36
, pp. 694
–708
.6.
Barun
, P.
, and Dwivedy
, S. K.
, 2009, “Nonlinear Vibration of a Magneto-Elastic Beam With Tip Mass
,” J. Vib. Acoust.
, 131
, p. 021011
.7.
Inoue
, T.
, Ishida
, Y.
, and Tsumura
, T.
, 2009, “Vibration of the Rigid Rotor Supported by a Repulsive Magnetic Bearing (Influence of Magnetic Anisotropies of Magnets)
,” J. Vib. Acoust.
, 131
, p. 031002
.8.
Caron
, J.-P.
, and Hauter
, J.-P.
, 1995, Modélisation et Commande de la Machine Asynchrone, Collection Méthodes et Pratiques de l’Ingénieur,
Edition Technip.
, Paris
.9.
Mimouni
, M. F.
, Mansouri
, M. N.
, Benghanem
, B.
, and Annabi
M.
, 2004, “Vectorial Command of an Asynchronous Motor fed by a Photovoltaic Generator
,” Renewable Energy
, 29
, pp. 433
–442
.10.
Yamapi
, R.
, and Woafo
, P.
, 2008, Mechanical Vibrations: Measurement, Effects and Control
, R. C.
Sapri
, ed., Nova Publishers
, pp. 419
–502
.11.
Kitio Kwuimy
, C. A.
, and Woafo
, P.
, 2008, “Dynamics, Chaos and Synchronization of Self-Sustained Electromechanical Systems With Clamped-Free Flexible Arm
,” Nonlinear Dyn.
, 53
, pp. 201
–213
.12.
Leung
, A. Y. T.
, and Chui
, S. K.
, 1995, “Non-Linear Vibration of Coupled Duffing Oscillators by an Improved Incremental Harmonic Balance Method
,” J. Sound Vibr.
, 181
, pp. 619
–633
.13.
Musielak
, D. E.
, Musielak
, Z. E.
, and Benner
, J. W.
, 2005, “Chaos and Routes to Chaos in Coupled Duffing Oscillators With Multiple Degrees of Freedom
,” Chaos, Solitons Fractals
, 24
, pp. 907
–922
.14.
Hayashi
, C.
, 1964, Nonlinear Oscillations in Physical Systems
, Mc-Graw-Hill
, New York
.15.
Nayfeh
, A. H.
, and Mook
, D. T.
, 1979, Nonlinear Oscillations
, Wiley-Interscience
, New York
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
