Dynamics of a discontinuous coupled electro-mechanical system oscillator with strong irrational nonlinearities and with two outputs
1Department of industrial engineering and maintenance, polytechnic university of Mongo, Chad
2Research unit of industrial systems engineering and environment (RU-ISEE), Fotso Victor University Institute of Technology, University of Dschang, Cameroon.
3Department of Mechanical Engineering, the University Institute of Technology, P.O. Box 455, The University of Ngaoundéré, Cameroon
4Department of Civil Engineering, Higher Teacher Training College of the Technical Education, P.O. Box 1872, University of Douala, Cameroon
5Department of technical sciences, faculty of exact and applied sciences, P.O. Box 4377 University of Djamena, Chad
Research Article
Global Journal of Engineering and Technology Advances, 2021, 06(01), 116-135.
Article DOI: 10.30574/gjeta.2021.6.1.0301
Publication history:
Received on 17 January 2021; revised on 24 January 2021; accepted on 26 January 2021
Abstract:
The dynamics of the nonlinear electromechanical device, consisting of a mechanical part with two outputs and an electrical part which acts as the server is strongly investigated in the present work. The mechanical part consists of two nonlinear oscillators with strong irrational nonlinearities having smooth or discontinuous characteristics, where nonlinearity is just due to the inclination of springs, the geometric configuration, which are both elastically coupled. While the electrical part is the 
Rayleigh equation. By using the Lagrangian formulation, the model equations are established and used to investigate the equilibrium points and their stabilities. Nest by using the multiple time scales method, the analytical solutions are found both for the case of large amplitude and the weak amplitude, leading to interesting bifurcation sets of the equilibria by varying the control parameters, the inclination angles and driven frequency. Finally, numerical investigations of the exact equation of the system are used to justify the validity of analytical results and to find new phenomena such as chaotic impulses, chaotic bursting and the train of kink signal generations.
Rayleigh equation. By using the Lagrangian formulation, the model equations are established and used to investigate the equilibrium points and their stabilities. Nest by using the multiple time scales method, the analytical solutions are found both for the case of large amplitude and the weak amplitude, leading to interesting bifurcation sets of the equilibria by varying the control parameters, the inclination angles and driven frequency. Finally, numerical investigations of the exact equation of the system are used to justify the validity of analytical results and to find new phenomena such as chaotic impulses, chaotic bursting and the train of kink signal generations.Keywords:
Irrational Nonlinearity; Electromechanical Device; Chaotic Impulse; Chaotic Bursting.
Full text article in PDF:
Copyright information:
Copyright © 2021 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0