Homotopy perturbation for conservative Helmholtz-Duffing oscillators

A. Y T Leung, Zhongjin Guo

    Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

    40 Citations (Scopus)

    Abstract

    The approximate periodic solutions of the Helmholtz-Duffing oscillator are obtained by homotopy perturbation. The Helmholtz-Duffing oscillator becomes a Duffing oscillator when the homotopy parameter degenerates to one and a Helmholtz oscillator when it is zero. Since the behaviors of the solutions in the positive and negative directions are quite different, the asymmetric equation is separated into two auxiliary equations. The auxiliary equations are solved by homotopy perturbation method. A new analytical period for the Helmholtz-Duffing equation is derived. The resulting second-order approximate periodic solutions are compared to the analytical solutions using numerical integration with improved accuracy over some existing methods. Thus, the homotopy perturbation is very effective for the asymmetric nonlinear oscillators. © 2009 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)287-296
    JournalJournal of Sound and Vibration
    Volume325
    Issue number1-2
    DOIs
    Publication statusPublished - 7 Aug 2009

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