Noisy Nonlinear Motions of Moored System. Part I: Analysis and Simulations
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123, Issue 5
Abstract
Nonlinear responses of a submerged moored structure are investigated taking into account the presence of environment random noise. Sources of nonlinearity of the system include a quadratic Morison hydrodynamic damping and a geometrically nonlinear restoring force. The random perturbations are modeled by a white-noise process to examine their effects on nonlinear responses analytically and numerically. The analysis procedure includes a generalized Melnikov process to study response stabilities in a global sense and the Fokker-Planck equation to demonstrate response characteristics from a probabilistic perspective. Rich nonlinear phenomena including bifurcations, coexistence of attractors, and chaos are identified and demonstrated. Probability density functions solved from the Fokker-Planck equation are used to depict (co)existing response attractors on the Poincaré section and demonstrate their probabilistic properties. Noise effects on responses are shown via a generalized Melnikov criterion and the probability density function. It is found that the presence of noise may expand the chaotic domain in the parameter space and also cause transitions between coexisting responses.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bernitsas, M. M., and Chung, J. S.(1990). “Nonlinear stability and simulation of two-line ship: towing and mooring.”Appl. Oc. Res., 11, 153–166.
2.
Bishop, S. R., and Virgin, L. N.(1988). “The onset of chaotic motions of a moored semi-submersible.”J. Offshore Mechanics and Arctic Engrg., 110, 205–209.
3.
Gottlieb, O. (1991). “Nonlinear oscillations, bifurcation and chaos in ocean mooring systems,” PhD thesis, Oregon State Univ., Corvallis, Oreg.
4.
Gottlieb, O., and Yim, S. C. S.(1992). “Nonlinear oscillations, bifurcations and chaos in a multi-point mooring system with a geometric nonlinearity.”Appl. Oc. Res., 14, 241–257.
5.
Gottlieb, O., and Yim, S. C. S.(1993). “Drag-induced instability and chaos in mooring systems.”J. Oc. Engrg., 29, 569–599.
6.
Isaacson, M.(1979). “Nonlinear inertia forces on bodies.”J. Wtrwy., Port, Coast. and Oc. Div., ASCE, 103, 213–227.
7.
Jordan, D. W., and Smith, P. (1987). Nonlinear ordinary differential equations, 2nd Ed., Oxford University Press.
8.
Kapitaniak, T. (1988). Chaos in systems with noise. World Scientific, Singapore.
9.
Lin, H., and Yim, S. C. S.(1995). “Chaotic roll motion and capsizing of ships under periodic excitation with random noise.”Appl. Oc. Res., 17(3), 185–204.
10.
Meirovitch, L. (1970). Method of analytical dynamics. McGraw-Hill, Inc., New York, N.Y.
11.
Moon, F. C. (1987). Chaotic vibrations: an introduction for applied scientists and engineers. John Wiley & Sons, New York, N.Y.
12.
Risken, H. (1984). The Fokker-Planck equation: methods of solution and applications. Springer-Verlag, Berlin, Germany.
13.
Stratonovich, R. L. (1967). Topics in the theory of random noise I. Gordon & Breach Science Publishers, New York, N.Y.
14.
Thompson, J. M. T.(1983). “Complex dynamics of compliant offshore structures.”Proc., Royal Soc. London A, 387, 407–427.
15.
Wiggins, S. (1990). Introduction to applied nonlinear dynamical systems and chaos. Springer-Verlag, New York, N.Y.
16.
Yim, S. C. S., and Lin, H. (1992). “Probabilistic analysis of a chaotic dynamical system.”Applied chaos, John Wiley & Sons, New York, N.Y., 219–241.
17.
Yim, S. C. S., Myrum, M. A., Gottlieb, O., Lin, H., and Shih, I.-M. (1993). “Summary and preliminary analysis of nonlinear oscillations in a submerged mooring system experiment.”Rep. No. OE-93-03, Ocean Engineering Program, Oregon State Univ., Corvallis, Oreg.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 123 • Issue 5 • September 1997
Pages: 287 - 295
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Sep 1, 1997
Published in print: Sep 1997
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.