Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T05:51:44.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Identification for Chaos and Subharmonic Responses in Coupled Forced Duffing's Oscillators

Published online by Cambridge University Press:  31 March 2011

J.-D. Jeng ,
Y. Kang  and
Y.-P. Chang
J.-D. Jeng
Affiliation:
Department of Mechanical Engineering, National United University, Miaoli, Taiwan 36003, R.O.C.
Y. Kang*
Affiliation:
Department of Mechanical Engineering, Chung Yuan Christian University, Chungli, Taiwan 32023, R.O.C.
Y.-P. Chang
Affiliation:
Department of Mechanical Engineering, Chung Yuan Christian University, Chungli, Taiwan 32023, R.O.C.
*
**Professor, corresponding author
Get access

Abstract

In this paper, a response integral quantity method is proposed. This technique provides a quantitative characterization of system responses and can assist the role of the traditional stroboscopic technique (Poincaré section method) in observing bifurcations and chaos of the nonlinear oscillators. We numerically analyze and identify the chaos and subharmonic responses in the forced coupled Duffing's oscillators in which we find that chaotic behaviors and high-order subharmonic responses exist. Due to the signal response contamination of system, it is difficult to identify the high-order responses of the subharmonic motion because of the sampling points on Poincaré map being very close to each other. Even the system responses are subject to misjudgments. The simulation results, however, show that the highorder subharmonic and chaotic responses and their bifurcations can be observed effectively.

Keywords

Response integral quantity methodPoincaré section methodForced coupled Duffing's oscillatorsSubharmonic response
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 1 , March 2011 , pp. 139 - 147
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Kapitaniak, T., “Stochastic Response with Bifurcations to Non-linear Duffing's Oscillator,” Journal of Sound and Vibration, 102, pp. 440–441 (1985).CrossRefGoogle Scholar
2.Fang, T. and Dowell, E. H., “Numerical Simulations of Periodic and Chaotic Responses in a Stable Duffing System,” International Journal of Non-Linear Mechanics, 22, pp. 401–425 (1987).CrossRefGoogle Scholar
3.Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, New York (1990).CrossRefGoogle Scholar
4.Jackson, E. A., Perspectives of Nonlinear Dynamics, Cambridge University Press, New York (1991).Google Scholar
5.Guckenheimer, J. and Holmes, P., “Nonlinear Oscillation and Bifurcation of Vector Fields,” Springer, New York (1993).Google Scholar
6.Sarma, M. S. and Rao, H. N., “A Rational Harmonic Balance Approximation for the Duffing Equation of Mixed Parity,” Journal of Sound and Vibration, 207, pp. 597–599 (1997).CrossRefGoogle Scholar
7.Mickens, R. E., “Mathematical and Numerical Study of the Duffing-harmonic Oscillator,” Journal of Sound and Vibration, 244, pp. 563–567 (2001).CrossRefGoogle Scholar
8.Hong, L. and Xu, J., “A Chaotic Crisis between Chaotic Saddle and Attractor in Forced Duffing Oscillators,” Communication in Nonlinear Science and Numerical Simulation, 9, pp. 313–329 (2004).CrossRefGoogle Scholar
9.Jing, L. and Wang, R., “Complex Dynamics in Duffing System with Two External Forcings,” Chaos, Solitons and Fractals, 23, pp. 399–411 (2005).CrossRefGoogle Scholar
10.Pezeshki, C. and Dowell, E. H., “On Chaos and Fractal Behavior in a Generalized Duffing's System,” Physica D, 32, pp. 194–209 (1988).CrossRefGoogle Scholar
11.Leung, A. Y. T. and Fung, T. C., “Construction of Chaotic Regions,” Journal of Sound and Vibration, 86, pp. 445–455 (1989).CrossRefGoogle Scholar
12.Dooren, R. V. and Janssen, H., “A Continuation Algorithm for Discovering New Chaotic Motion in Forced Duffing Systems,” Journal of Computational and Applied Mathematics, 66, pp. 527–541 (1996).CrossRefGoogle Scholar
13.Kim, Y., Lee, S. Y. and Kim, S. Y., “Experimentally Observation of Dynamic Stabilization in a Double-well Duffing Oscillator,” Physics Letters A, 275, pp. 254–259 (2000).CrossRefGoogle Scholar