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Frequency control of singularly perturbed forced duffing’s oscillator

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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.

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  1. Institute of Applied Informatics, Automation and Mathematics, Faculty of Materials Science and Technology, Hajdoczyho 1, 917 01, Trnava, Slovakia

    R. Vrabel & M. Abas

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  1. R. Vrabel
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  2. M. Abas
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Correspondence to R. Vrabel.

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Vrabel, R., Abas, M. Frequency control of singularly perturbed forced duffing’s oscillator. J Dyn Control Syst 17, 451–467 (2011). https://doi.org/10.1007/s10883-011-9125-0

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  • DOI: https://doi.org/10.1007/s10883-011-9125-0

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