This paper studies the dynamics of a self-sustained electromechanical transducer. The stability of fixed points in the linear response is examined. Their local bifurcations are investigated and different types of bifurcation likely to occur are found. Conditions for the occurrence of Hopf bifurcations are derived. Harmonic oscillatory solutions are obtained in both nonresonant and resonant cases. Their stability is analyzed in the resonant case. Various bifurcation diagrams associated to the largest one-dimensional (1-D) numerical Lyapunov exponent are obtained, and it is found that chaos can appear suddenly, through period doubling, period adding, or torus breakdown. The extreme sensitivity of the electromechanical system to both initial conditions and tiny variations of the coupling coefficients is also outlined. The experimental study of̱the electromechanical system is carried out. An appropriate electronic circuit (analog simulator) is proposed for the investigation of the dynamical behavior of the electromechanical system. Correspondences are established between the coefficients of the electromechanical system model and the components of the electronic circuit. Harmonic oscillatory solutions and phase portraits are obtained experimentally. One of the most important contributions of this work is to provide a set of reliable analytical expressions (formulas) describing the electromechanical system behavior. These formulas are of great importance for design engineers as they can be used to predict the states of the electromechanical systems and respectively to avoid their destruction. The reliability of the analytical formulas is demonstrated by the very good agreement with the results obtained by both the numeric and the experimental analysis.
Skip Nav Destination
e-mail: chedjou@ictp.it; chedjou@ant.uni-hannover.de; chedjou@moniut.univ-bpclermont.fr
e-mail: kya@ant.uni-hannover.de
e-mail: moussaildoko@yahoo.fr
e-mail: ku@ant.uni-hannover.de
e-mail: mathis@tet.uni-hannover.de
Article navigation
June 2006
Technical Papers
Behavior of a Self-Sustained Electromechanical Transducer and Routes to Chaos
J. C. Chedjou,
e-mail: chedjou@ictp.it; chedjou@ant.uni-hannover.de; chedjou@moniut.univ-bpclermont.fr
J. C. Chedjou
International Centre for Theoretical Physics (ICTP)
, Strada Costiera 11, 34014 Trieste, Italy, IUT-LEM
, 03100 Montluçon Cedex, France, and Department of Physics, Faculty of Science, University of Dschang
, BP 67, Dschang, Cameroon
Search for other works by this author on:
K. Kyamakya,
K. Kyamakya
Chair of Computer Science in Transportation, Institut fü. Informatik-systeme,
e-mail: kya@ant.uni-hannover.de
University of Klagenfurt
, Universitaetsstr. 65, A-9020 Klagenfurt, Austria
Search for other works by this author on:
I. Moussa,
I. Moussa
Department of Physics, Faculty of Science,
e-mail: moussaildoko@yahoo.fr
University of Yaoundé-I
, BP 812, Yaoundé, Cameroon
Search for other works by this author on:
H.-P. Kuchenbecker,
H.-P. Kuchenbecker
Institut für Allgemeine Nachrichtentechnik,
e-mail: ku@ant.uni-hannover.de
Univeristät Hannover
, Appelstr. 9A, 30167, Hannover, Germany
Search for other works by this author on:
W. Mathis
W. Mathis
Institut für Theoretische Elektrotechnik und Hochfrequenztechnik,
e-mail: mathis@tet.uni-hannover.de
University of Hannover
, Appelstr. 9A, 30167, Hannover, Germany
Search for other works by this author on:
J. C. Chedjou
International Centre for Theoretical Physics (ICTP)
, Strada Costiera 11, 34014 Trieste, Italy, IUT-LEM
, 03100 Montluçon Cedex, France, and Department of Physics, Faculty of Science, University of Dschang
, BP 67, Dschang, Cameroone-mail: chedjou@ictp.it; chedjou@ant.uni-hannover.de; chedjou@moniut.univ-bpclermont.fr
K. Kyamakya
Chair of Computer Science in Transportation, Institut fü. Informatik-systeme,
University of Klagenfurt
, Universitaetsstr. 65, A-9020 Klagenfurt, Austriae-mail: kya@ant.uni-hannover.de
I. Moussa
Department of Physics, Faculty of Science,
University of Yaoundé-I
, BP 812, Yaoundé, Cameroone-mail: moussaildoko@yahoo.fr
H.-P. Kuchenbecker
Institut für Allgemeine Nachrichtentechnik,
Univeristät Hannover
, Appelstr. 9A, 30167, Hannover, Germanye-mail: ku@ant.uni-hannover.de
W. Mathis
Institut für Theoretische Elektrotechnik und Hochfrequenztechnik,
University of Hannover
, Appelstr. 9A, 30167, Hannover, Germanye-mail: mathis@tet.uni-hannover.de
J. Vib. Acoust. Jun 2006, 128(3): 282-293 (12 pages)
Published Online: November 16, 2005
Article history
Received:
July 11, 2003
Revised:
November 16, 2005
Citation
Chedjou, J. C., Kyamakya, K., Moussa, I., Kuchenbecker, H., and Mathis, W. (November 16, 2005). "Behavior of a Self-Sustained Electromechanical Transducer and Routes to Chaos." ASME. J. Vib. Acoust. June 2006; 128(3): 282–293. https://doi.org/10.1115/1.2172255
Download citation file:
Get Email Alerts
Related Articles
Multiple Stability and Unpredictable Outcomes in the Chaotic Vibrations of Euler Beams
J. Vib. Acoust (January,2002)
Analysis of a Chaotic Electrostatic Micro-Oscillator
J. Comput. Nonlinear Dynam (January,2011)
Dynamics of a Quasiperiodically Forced Rayleigh Oscillator
J. Dyn. Sys., Meas., Control (September,2006)
Effect of Boundary Conditions on Nonlinear Vibrations of Circular Cylindrical Panels
J. Appl. Mech (July,2007)
Related Proceedings Papers
Related Chapters
Dynamic Behavior in a Singular Delayed Bioeconomic Model
International Conference on Instrumentation, Measurement, Circuits and Systems (ICIMCS 2011)
A Coordination Model for Multi Agent System by Developing Linda
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)
Accommodation and Stability of Alloying Elements in Amorphous Grain Boundaries of Zirconia
Zirconium in the Nuclear Industry: 20th International Symposium