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  • Open Access

    ARTICLE

    Damped Mathieu Equation with a Modulation Property of the Homotopy Perturbation Method

    Yusry O. El-Dib, Nasser S. Elgazery*

    Sound & Vibration, Vol.56, No.1, pp. 21-36, 2022, DOI:10.32604/sv.2022.014166

    Abstract In this article, the main objective is to employ the homotopy perturbation method (HPM) as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients. As a simple example, the nonlinear damping Mathieu equation has been investigated. In this investigation, two nonlinear solvability conditions are imposed. One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases. The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the first-order solvability condition. The approach… More >

  • Open Access

    ARTICLE

    Dynamic Response and Oscillating Behaviour of Fractionally Damped Beam

    Diptiranjan Behera1, S. Chakraverty2

    CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.3, pp. 211-225, 2015, DOI:10.3970/cmes.2015.104.211

    Abstract This paper presents the numerical solution of a viscoelastic continuous beam whose damping behaviours are defined in term of fractional derivatives of arbitrary order. Homotopy Perturbation Method (HPM) is used to obtain the dynamic response with respect to unit impulse load. Obtained results are depicted in term of plots. Comparisons are made with the analytic solutions obtained by Zu-feng and Xiao-yan (2007) to show the effectiveness and validation of the present method. More >

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