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Frequency control of singularly perturbed forced duffing’s oscillator

  • R. Vrabel
  • M. Abas
Article

Abstract

We analyze the dynamics of the forced singularly perturbed differential equation of Duffing’s type. We explain the appearance of the large frequency nonlinear oscillations of the solutions. It is shown that the frequency can be controlled by a small parameter at the highest derivative. We give some generalizations of results obtained recently by B. S. Wua, W. P. Suna, and C. W. Lim. Analytical approximations to the double-well Duffing oscillator in large amplitude oscillations (see J. Sound Vibration 307 (2007), Nos. 3–5, 953–960). A new method for an analysis of the nonlinear oscillations which is based on the dynamic change of coordinates is proposed.

Key words and phrases

Singular perturbation Duffing’s oscillator 

2000 Mathematics Subject Classification

34A26 34A34 34C40 34K26 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institute of Applied Informatics, Automation and Mathematics, Faculty of Materials Science and TechnologyTrnavaSlovakia

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