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Confusion threshold study of the Duffing oscillator with a nonlinear fractional damping term
- Source :
- Journal of Low Frequency Noise, Vibration and Active Control, Vol 40 (2021)
- Publication Year :
- 2021
- Publisher :
- SAGE Publishing, 2021.
-
Abstract
- In this study, the critical conditions for generating chaos in a Duffing oscillator with nonlinear damping and fractional derivative are investigated. The Melnikov function of the Duffing oscillator is established based on Melnikov theory. The necessary analytical conditions and critical value curves of chaotic motion in the sense of Smale horseshoe are obtained. The numerical solutions of chaotic motion, including time history diagram, frequency spectrum diagram, phase diagram, and Poincare map, are studied. The correctness of the analytical solution is verified through a comparison of numerical and analytical calculations. The effects of linear and nonlinear parameters on chaotic motion are also analyzed. These results are relevant to the study of system dynamics.
Details
- Language :
- English
- ISSN :
- 14613484 and 20484046
- Volume :
- 40
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of Low Frequency Noise, Vibration and Active Control
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.88fe4ff3db4467976f304b1605281c
- Document Type :
- article
- Full Text :
- https://doi.org/10.1177/1461348420922686