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

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
.
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