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Complex dynamics of an archetypal self-excited SD oscillator driven by moving belt friction |
| Zhi-Xin Li(李志新)1, Qing-Jie Cao(曹庆杰)1, Léger Alain2 |
1. School of Astronautics, Harbin Institute of Technology, Harbin 150001, China;
2. Laboratoire de Mécanique et d'Acoustique, CNRS, 31, Chemin Joseph Aiguier, 13402 Marseille Cedex 20, France |
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Abstract We propose an archetypal self-excited system driven by moving belt friction, which is constructed with the smooth and discontinuous (SD) oscillator proposed by the Cao et al. and the classical moving belt. The moving belt friction is modeled as the Coulomb friction to formulate the mathematical model of the proposed self-excited SD oscillator. The equilibrium states of the unperturbed system are obtained to show the complex equilibrium bifurcations. Phase portraits are depicted to present the hyperbolic structure transition, the multiple stick regions, and the friction-induced asymmetry phenomena. The numerical simulations are carried out to demonstrate the friction-induced vibration of multiple stick-slip phenomena and the stick-slip chaos in the perturbed self-excited system. The results presented here provide an opportunity for us to get insight into the mechanism of the complex friction-induced nonlinear dynamics in mechanical engineering and geography.
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Received: 28 June 2015
Revised: 06 August 2015
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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05.45.Ac
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(Low-dimensional chaos)
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05.10.-a
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(Computational methods in statistical physics and nonlinear dynamics)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11372082 and 11572096) and the National Basic Research Program of China (Grant No. 2015CB057405). |
Corresponding Authors:
Qing-Jie Cao
E-mail: qingjiecao@hotmail.com
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Cite this article:
Zhi-Xin Li(李志新), Qing-Jie Cao(曹庆杰), Léger Alain Complex dynamics of an archetypal self-excited SD oscillator driven by moving belt friction 2016 Chin. Phys. B 25 010502
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