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Asymptotic solutions of coupled equations of supercritically axially moving beam

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Abstract

In supercritical regime, the coupled model equations for the axially moving beam with simple support boundary conditions are considered. The critical speed is determined by linear bifurcation analysis, which is in agreement with the results in the literature. For the corresponding static equilibrium state, the second-order asymptotic nontrivial solutions are obtained through the multiple scales method. Meantime, the numerical solutions are also obtained based on the finite difference method. Comparisons among the analytical solutions, numerical solutions and solutions of integro-partial-differential equation of transverse which is deduced from coupled model equations are made. We find that the second-order asymptotic analytical solutions can well capture the nontrivial equilibrium state regardless of the amplitude of transverse displacement. However, the integro-partial-differential equation is only valid for the weak small-amplitude vibration axially moving slender beams.

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Acknowledgments

This project was supported by the State Key Program of National Nature Science Foundation of China (No.11232009) and the Natural Science Foundation of China (Nos.11372171, 11422214 and 11472147) and Foundation of ShaoXing University (No.20145002).

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai, 200072, People’s Republic of China

    Yuanbin Wang, Hu Ding & Li-Qun Chen

  2. Department of Mathematics, ShaoXing University, ShaoXing, Zhejiang, People’s Republic of China

    Yuanbin Wang

  3. Department of Mechanics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Li-Qun Chen

Authors
  1. Yuanbin Wang
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  2. Hu Ding
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  3. Li-Qun Chen
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Correspondence to Hu Ding.

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Wang, Y., Ding, H. & Chen, LQ. Asymptotic solutions of coupled equations of supercritically axially moving beam. Nonlinear Dyn 87, 25–36 (2017). https://doi.org/10.1007/s11071-016-3021-9

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  • DOI: https://doi.org/10.1007/s11071-016-3021-9

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