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TECHNICAL PAPERS

Coupled Nonlinear Barge Motions, Part II: Stochastic Models and Stability Analysis

[+] Author and Article Information
Solomon C. S. Yim, Tongchate Nakhata

Ocean Engineering Program Oregon State University Corvallis, OR 97331

Erick T. Huang

1100 23rd Avenue Naval Facilities Engineering Service Center Port Hueneme, CA 93043-4370

J. Offshore Mech. Arct. Eng 127(2), 83-95 (May 27, 2005) (13 pages) doi:10.1115/1.1884617 History: Received August 06, 2003; Revised March 23, 2004; Online May 27, 2005
Copyright © 2005 by ASME
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References

Roberts,  J. B., 1982a, “A Stochastic Theory for Nonlinear Ship Rolling in Irregular Seas,” J. Ship Res., 26(4), pp. 229–245.
Roberts,  J. B., 1982b, “Effect of Parametric Excitation on Ship Rolling Motion in Random Waves,” J. Ship Res., 26(4), pp. 246–253.
Robert,  J. B., Dunne,  J. F., and Debonos,  A., 1994, “Stochastic Estimation Methods for Non-Linear Ship Roll Motion,” Probab. Eng. Mech., 9, pp. 83–93.
Dahle,  E. A., Myhaug,  D., and Dahl,  S. J., 1988, “Probability of Capsizing in Steep and High Waves From the Side in Open Sea and Coastal Waters,” Ocean Eng.,15(2), pp. 139–151.
Lin,  H., and Yim,  S. C. S., 1995, “Chaotic Roll Motion and Capsizing of Ships Under Periodic Excitation With Random Noise,” Appl. Ocean. Res., 17(3), pp. 185–204.
Falzarano,  J. M., Shaw,  S. W., and Troesch,  A. W., 1992, “Application of Global Methods for Analyzing Dynamical Systems to Ship Rolling Motion and Capsizing,” Int. J. Bifurcation Chaos Appl. Sci. Eng., 2(1), pp. 101–116.
Nayfeh,  A. H., and Sanchez,  N. E., 1990, “Stability and Complicated Rolling Responses of Ships in Regular Beam Sea,” Int. Shipbuilding Congress,37(412), pp. 331–352.
Kwon,  S. H., Kim,  D. W., and McGregor,  R. C., 1993, “A Stochastic Roll Response Analysis of Ships in Irregular Waves,” Int. J. Offshore Polar Eng., 3(1), pp. 32–34.
Cai, G. Q., Yu, S. J., and Lin, Y. K., 1994, “Ship Rolling in Random Sea,” Stochastic Dynamics and Reliability of Nonlinear Ocean Systems, ASME DE-Vol. 77, pp. 81–88.
Chakrabarti, S. K., 1994, Hydrodynamics of Offshore Structures, Computational Mechanics Publications, Southampton.
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Naess, A., and Johnsen, J. M., “Response Statistics of Nonlinear Dynamic Systems by Path Integrations,” IUTAM Symposium on Nonlinear Stochastic Mechanics, Torino, Italy, 1991, pp. 401–409.
Naess,  A., and Johnsen,  J. M., 1993, “Response Statistic of Nonlinear, Compliant Offshore Structures by the Path Integral Solution Method,” Probab. Eng. Mech., 8, 91–106.
Wissel,  C., 1979, “Manifolds of Equivalent Path Integral Solutions of the Fokker-Planck Equation,” Z. Phys. B, 35, pp. 185–191.
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Figures

Grahic Jump Location
Comparison of barge roll response time histories predicted by 2DOF and 1DOF models under (a) regular waves with H=6 ft. and T=8 s, and (b) random waves with Hs=4.7 ft. and Tp=8.2 s
Grahic Jump Location
Comparison of barge roll response time histories predicted by 2DOF and 1DOF models under (a) regular waves with H=6.5 ft. and T=6 s, and (b) random waves with Hs=5.5 ft. and Tp=6.0 s
Grahic Jump Location
(a) 1DOF model, and (b) 2DOF model path-integral solution prediction of probability density of roll response under random waves with Hs=4.7 ft. and Tp=8.2 s at time t=5 min
Grahic Jump Location
(a) 1DOF model, and (b) 2DOF model path-integral solution prediction of probability density of roll response under random waves with Hs=5.5 ft. and Tp=5.5 s at time t=5 min
Grahic Jump Location
Comparison of roll response marginal probability density between numerical predictions of 2DOF and 1DOF models at time t=5 min under random wave with (a) Hs=4.7 ft. and Tp=8.2 s, and (b) Hs=5.5 ft. and Tp=5.5 s
Grahic Jump Location
Comparison of measured experimental heave and wave time histories under (a) regular wave with H=6 ft. and T=6 s, and (b) random wave with Hs=4.7 ft. and Tp=8.2 s
Grahic Jump Location
Comparison of predicted barge roll response time histories predicted by 2DOF, 1DOF, and quasi-2DOF models; (a) regular waves with H=6.5 ft. and T=6 s, and (b) random waves with Hs=5.5 ft. and Tp=6.0 s
Grahic Jump Location
Comparison of roll response marginal density at 5 minutes predicted by 2DOF, 1 DOF, and quasi-2DOF models under random wave excitation with Hs=5.5 ft. and Tp=5.5 s
Grahic Jump Location
Analytical roll righting moment of barge considered
Grahic Jump Location
(a) Probability density, and (b) reliability against capsizing of barge roll response to sea state 1 random waves
Grahic Jump Location
(a) Probability density, and (b) reliability against capsizing of barge roll response to sea state 4 random waves
Grahic Jump Location
(a) Probability density, and (b) reliability against capsizing of barge roll response to sea state 7 random waves
Grahic Jump Location
(a) Probability density, and (b) reliability against capsizing of barge roll response to sea state 9 random waves
Grahic Jump Location
Mean time to reach specified capsizing probabilities for a barge operating in sea states 3 through 9 obtained using quasi-2DOF model

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