Higher-Order Approximation of Cubic-Quintic Duffing Model

S. S. Ganji, Amin Barari, H. Babazadeh, M. G. Sfahani, G. Domairry

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    10 Citationer (Scopus)

    Abstract

    We apply an Artificial Parameter Lindstedt-Poincaré Method (APL-PM) to find improved approximate solutions for strongly nonlinear Duffing oscillations with cubic-quintic nonlinear restoring force. This approach yields simple linear algebraic equations instead of nonlinear algebraic equations without analytical solution which makes it a unique solution. It is demonstrated that this method works very well for the whole range of parameters in the case of the cubic-quintic oscillator, and excellent agreement of the approximate frequencies with the exact one has been observed and discussed. Moreover, it is not limited to the small parameter such as in the classical perturbation method. Interestingly, this study revealed that the relative error percentage in the second-order approximate analytical period is less than 0.042% for the whole parameter values. In addition, we compared this analytical solution with the Newton-Harmonic Balancing Approach. Results indicate that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems. Utter simplicity of the solution procedure confirms that this method can be easily extended to other kinds of nonlinear evolution equations.
    OriginalsprogEngelsk
    TidsskriftJournal of Vibroengineering
    Vol/bind13
    Udgave nummer2
    Sider (fra-til)219-232
    Antal sider14
    ISSN1392-8716
    StatusUdgivet - 2011

    Emneord

    • Artificial Parameter Lindstedt-Poincaré Method (APL-PM)
    • Nonlinear Cubic-Quintic Oscillation
    • Duffing Equation

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