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Nonlinear oscillations with parametric excitation solved by homotopy analysis method

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Abstract

An analytical technique, namely the homotopy analysis method (HAM), is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small physical parameters at all, and thus valid for both weakly and strongly nonlinear problems. In addition, HAM is different from all other analytic techniques in providing a simple way to adjust and control convergence region of the series solution by means of an auxiliary parameter \({\hbar}\) . In the present paper, a periodic analytic approximations for nonlinear oscillations with parametric excitation are obtained by using HAM, and the results are validated by numerical simulations.

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Authors and Affiliations

  1. School of Shipbuilding Engineering, Harbin Institute of Technology at Weihai, Weihai, 264209, China

    Jianmin Wen

  2. CIMS Research Center, Tongji University, Shanghai, 200092, China

    Zhengcai Cao

Authors
  1. Jianmin Wen
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  2. Zhengcai Cao
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Correspondence to Jianmin Wen.

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The English text was polished by Yunming Chen.

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Wen, J., Cao, Z. Nonlinear oscillations with parametric excitation solved by homotopy analysis method. Acta Mech Sin 24, 325–329 (2008). https://doi.org/10.1007/s10409-008-0143-4

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  • DOI: https://doi.org/10.1007/s10409-008-0143-4

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