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Stability analysis of nonlinear ship-roll dynamics under wind and wave

Author

Listed:
  • Liu, Yachong
  • Hu, Ankang
  • Han, Fenglei
  • Lu, Yu

Abstract

Considering the nonlinear damping and restoring moments, a nonlinear ship rolling dynamical system is established in this paper. When only subjected to periodic wave excitation, the system is symmetric, whereas when subjected to joint action of periodic wave excitation and crosswind, the system degenerates into asymmetric. The simple zero points of Melnikov function in both two kinds of dynamical systems are computed by virtue of Gauss–Legendre integration. As a numerical verification of the threshold value, Lyapunov exponents are computed. In the end of the paper, the motion stability and the effect of crosswind on stability are analyzed by means of safe basin simulation and observation of its gradual erosion phenomenon. The study shows that crosswind results in symmetry breaking and further reduces the stability of the rolling system.

Suggested Citation

  • Liu, Yachong & Hu, Ankang & Han, Fenglei & Lu, Yu, 2015. "Stability analysis of nonlinear ship-roll dynamics under wind and wave," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 32-39.
    • Handle: RePEc:eee:chsofr:v:76:y:2015:i:c:p:32-39
    DOI: 10.1016/j.chaos.2015.03.011
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    References listed on IDEAS

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    1. Cao, Hongjun & Seoane, Jesús M. & Sanjuán, Miguel A.F., 2007. "Symmetry-breaking analysis for the general Helmholtz–Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 197-212.
    2. Feng, Jingjing & Zhang, Qichang & Wang, Wei, 2012. "Chaos of several typical asymmetric systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(7), pages 950-958.
    3. Sofroniou, Anastasia & Bishop, Steven R., 2006. "Breaking the symmetry of the parametrically excited pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 673-681.
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