Browse > Article
http://dx.doi.org/10.7837/kosomes.2018.24.2.140

Dynamical Analysis of the Mooring Vessel System Under Surge Excitations  

Lee, Sang-Do (Graduate School of Korea Maritime and Ocean University)
You, Sam-Sang (Division of Mechanical Engineering, Korea Maritime and Ocean University)
Publication Information
Journal of the Korean Society of Marine Environment & Safety / v.24, no.2, 2018 , pp. 140-145 More about this Journal
Abstract
This paper deals with the dynamical analysis of a two-point mooring vessel under surge excitations. The characteristics of nonlinear behaviors are investigated completely including bifurcation and limit cycle according to particular input parameter changes. The strong nonlinearity of the mooring system is mainly caused by linear and cubic terms of restoring force. The numerical simulation is performed based on the fourth order Runge-Kutta algorithm. The bifurcation diagram and several instability phenomena are observed clearly by varying amplitudes as well as frequencies of surge excitations. Stable periodic solutions, called the periodic windows, can be obtained in succession between chaotic clouds of dots in case of frequency ${\omega}=0.4rad/s$. In addition, the chaotic region is unexpectedly increased when external forcing amplitude exceeds 1.0 with the angular frequency of ${\omega}=0.7rad/s$. Compared to the cases for ${\omega}=0.4$, 0.7rad/s, the region of chaotic behavior becomes more fragile than in the case of ${\omega}=1.0rad/s$. Finally, various types of steady states including sub-harmonic motion, limit cycle, and symmetry breaking phenomenon are observed in the two-point mooring system at each parameter value.
Keywords
Two-point mooring system; Nonlinear behavior; Bifurcation; Chaos; Limit cycle; Sub-harmonic;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Akhmet, M. U. and M. O. Fen(2012), Chaotic Period-Doubling and OGY Control for the Forced Duffing Equation, Journal of Communications in Nonlinear Science and Numerical Simulation, Vol. 17, pp. 1929-1946.   DOI
2 Banik, A. K. and T. K. Datta(2010), Stability Analysis of Two-Point Mooring System in Surge Oscillation, Journal of Computational and Nonlinear Dynamics, Vol. 5, pp. 1-8 (021005).
3 Belato, D., H. I. Weber, J. M. Balthazar and D. T. Mook(2001), Chaotic Vibrations of a Nonideal Electro-Mechanical System, Journal of Solids and Structures, Vol. 38, pp. 1699-1706.   DOI
4 Ellermann, K.(2005), Dynamics of a Moored Barge under Periodic and Randomly Disturbed Excitation, Ocean Engineering, Vol. 32, pp. 1420-1430.   DOI
5 Gottlieb, O.(1991), Nonlinear Oscillations, Bifurcations and Chaos in Ocean Mooring Systems, Doctoral Dissertation, Oregon State University, p. 28.
6 Gottlieb, O. and S. C. S. Yim(1992), Nonlinear Oscillations, Bifurcations and Chaos in a Multi-Point Mooring System with a Geometric Nonlinearity, Applied Ocean Research, Vol. 14, pp. 241-257.   DOI
7 Gottlieb, O. and S. C. S. Yim(1997), Nonlinear Dynamics of a Coupled Surge-Heave Small-Body Ocean Mooring System, Ocean Engineering, Vol. 24. No. 5, pp. 479-495.   DOI
8 King, P. E. and S. C. Yim(2007), Stochastic Control of Sensitive Nonlinear Motions of an Ocean Mooring System, Journal of Offshore Mechanics and Arctic Engineering, Vol. 129, pp. 29-38.   DOI
9 Mitra, R. K., A. K. Banik and S. Chatterjee(2017), State Feedback Control of Surge Oscillations of Two-Point Mooring System, Journal of Sound and Vibration, Vol. 386, pp. 1-20.   DOI
10 Ueda, Y.(1991), Survey of Regular and Chaotic Phenomena in the Forced Duffing Oscillator, Journal of Chaos, Solitons & Fractals, Vol. 1, No. 3, pp. 199-231.   DOI
11 Umar, A. and T. K. Datta(2003), Nonlinear Response of a Moored Buoy, Ocean Engineering, Vol. 30, No. 13, pp. 1625-1646.   DOI
12 Umar, A., T. K. Datta and S. Ahmad(2010), Complex Dynamics of Slack Mooring System Under Wave and Wind Excitations, The Open Oceanography Journal, Vol. 4, pp. 9-31.   DOI
13 Zou, K. and S. Nagarajaiah(2015), An Analytical Method for Analyzing Symmetry-Breaking Bifurcation and Period-Doubling Bifurcation, Journal of Communications in Nonlinear Science and Numerical Simulation, Vol. 22, pp. 780-792.   DOI