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Dynamic Analysis of Generalized Conservative Nonlinear Oscillators Via Frequency Amplitude Formulation

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Abstract

In this paper, two kinds of frequency–amplitude formulation are used to solve the generalized conservative nonlinear equation in the form of \({{u}^{\prime\prime}+u+u^{2n-1}\sqrt{1+\varepsilon^{2}u^{4m}}=0}\) for any arbitrary power of n and m. This equation is a general form of plasma physics equations and the Duffing equation. A frequency analysis is carried out and the relationship between the angular frequency and the initial amplitude is obtained in closed analytical form. This equation is analyzed in three cases: as a plasma physics equation, as a higher order Duffing equation and as an equation with irrational restoring force. Comparison with the exact integration method is also made, revealing that the present method leads to accurate solutions.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Y. Khan

  2. Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran

    M. Kalami-Yazdi

  3. School of Railway Engineering, Iran University of Science and Technology, Narmak, Tehran, 16846, Iran

    H. Askari & Z. Saadatnia

Authors
  1. Y. Khan
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  2. M. Kalami-Yazdi
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  3. H. Askari
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  4. Z. Saadatnia
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Correspondence to Y. Khan.

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Khan, Y., Kalami-Yazdi, M., Askari, H. et al. Dynamic Analysis of Generalized Conservative Nonlinear Oscillators Via Frequency Amplitude Formulation. Arab J Sci Eng 38, 175–179 (2013). https://doi.org/10.1007/s13369-011-0035-y

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  • DOI: https://doi.org/10.1007/s13369-011-0035-y

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