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Vertical vibration of strip mill with the piecewise nonlinear constraint arising from hydraulic cylinder

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Abstract

Vertical vibration model of strip mill is established by considering piecewise nonlinear constraint arising from hydraulic cylinder. The approximate analytical solution of the model is obtained by incremental harmonic balance (IHB) method. The harmonic frequencies not conducive to stability are produced because the nonlinearity of the piecewise constraint. Bifurcation behavior of the system changes with external excitation amplitude and frequency ratio, intermittent chaos and periodic window are appeared alternately, the chaos region enlarged with the increasing piecewise interval. Compared with the piecewise linear constraint, the region of chaotic motion is widened obviously under the nonlinear constraint. Moreover, the critical condition of bifurcation and chaos behavior can be obtained from maximum Lyapunov exponent (MLE).

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Authors and Affiliations

  1. School of Information Science and Engineering, Yanshan University, Qinhuangdao, 066004, China

    Fei Liu, Bin Liu & Hao-ran Liu

  2. The Key Laboratory for Special Fiber and Fiber Sensor of Hebei Province, Yanshan University, Qinhuangdao, 066004, China

    Fei Liu, Bin Liu & Hao-ran Liu

  3. Hebei Iron & Steel Group CO., Ltd., Chengde Iron & Steel Company, Chengde, 067000, China

    Yan-ling Gong & Song-jun Wang

Authors
  1. Fei Liu
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  2. Bin Liu
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  3. Hao-ran Liu
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Correspondence to Hao-ran Liu.

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Liu, F., Liu, B., Liu, Hr. et al. Vertical vibration of strip mill with the piecewise nonlinear constraint arising from hydraulic cylinder. Int. J. Precis. Eng. Manuf. 16, 1891–1898 (2015). https://doi.org/10.1007/s12541-015-0246-3

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  • DOI: https://doi.org/10.1007/s12541-015-0246-3

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