Analytical expressions of the necessary and sufficient conditions for stability of mooring systems representing bifurcation boundaries, and expressions defining the morphogeneses occurring across boundaries are presented. These expressions provide means for evaluating the stability of a mooring system around an equilibrium position and constructing catastrophe sets in any parametric design space. These expressions allow the designer to select appropriate values for the mooring parameters without resorting to trial and error. A number of realistic applications are provided for barge and tanker mooring systems which exhibit qualitatively different nonlinear dynamics. The mathematical model consists of the nonlinear, third-order maneuvering equations of the horizontal plane slow-motion dynamics of a vessel moored to one or more terminals. Mooring lines are modeled by synthetic nylon ropes, chains, or steel cables. External excitation consists of time-independent current, wind, and mean wave drift forces. The analytical expressions presented in this paper apply to nylon ropes and current excitation. Expressions for other combinations of lines and excitation can be derived.
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Research Papers
1.
Abkowitz, M. A., Stability and Motion Control of Ocean Vehicles, MIT Press, Cambridge, 1972.
2.
Abkowitz
M. A.
Measurement of Hydrodynamic Characteristics from Ship Maneuvering Trials by System Identification
,” SNAME Transactions
, Vol. 88
, 1980
, pp. 283
–318
.3.
API, “Analysis of Spread Mooring Systems for Floating Drilling Units,” API Recommended Practice 2P (RP2P), Second Edition, May 1987.
4.
API, “Draft Recommended Practice for Design and Analysis of Stationkeeping Systems for Floating Structures,” API Recommended Practice, May 1994.
5.
Benford
H.
The Control of Yaw in Towed Barges
,” International Shipbuilding Progress
, Vol. 2
, No. 11
, 1955
, pp. 296
–318
.6.
Bernitsas
M. M.
Chung
J. S.
Nonlinear Stability and Simulation of Two-Line Ship Towing and Mooring
,” Journal of Applied Ocean Research
, Vol. 12
, No. 2
, April 1990
, pp. 77
–92
.7.
Bernitsas
M. M.
Garza-Rios
L. O.
Effect of Mooring Line Arrangement on the Dynamics of Spread Mooring Systems
,” ASME JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING
, Vol. 118
, No. 1
, Feb. 1996
, pp. 7
–20
.8.
Bernitsas
M. M.
Kekridis
N. S.
Simulation and Stability of Ship Towing
,” International Shipbuilding Progress
, Vol. 32
, No. 369
, 1986
, pp. 112
–123
.9.
Bernitsas, M. M., and Papoulias, F. A., “Nonlinear Stability and Maneuvering Simulation of Single Point Mooring Systems,” Proceedings of Offshore Station Keeping Symposium, SNAME, Houston, TX, February 1–2, 1990, pp. 1–19.
10.
Brix, J. E., “Lighters and Seagoing Barges and the Design of Yaw Controlling Units,” 2nd International Tug Conference, London, U.K., Oct. 1971.
11.
Cox, J. V., “Statmoor-A Single Point Mooring Static Analysis Program,” Naval Civil Engineering Laboratory, Report No. AD-A119 979, June 1982.
12.
Chung
J. S.
Bernitsas
M. M.
Dynamics of Two-Line Ship Towing/Mooring Systems: Bifurcations, Singularities of Stability Boundaries, Chaos
,” Journal of Ship Research
, SNAME, Vol. 36
, No. 2
, June 1992
, pp. 93
–105
.13.
D’Azzo, J. J., and Houpis, C. H., Linear Control System Analysis Design, McGraw-Hill, New York, NY, 1975.
14.
Eda
H.
Low Speed Controllability of Ships in Wind
,” Journal of Ship Research
, Vol. 12
, No. 3
, Sept. 1968
, pp. 181
–200
.15.
Garza-Rios
L. O.
Bernitsas
M. M.
Analytical Expressions of the Bifurcation Boundaries for Symmetric Spread Mooring Systems
,” Journal of Applied Ocean Research
, Vol. 17
, No. 6
, Dec. 1995
, pp. 325
–341
.16.
Garza-Rios
L. O.
Bernitsas
M. M.
Analytical Expressions of the Stability and Bifurcation Boundaries for General Spread Mooring Systems
,” Journal of Ship Research
, Vol. 40
, No. 4
, Dec. 1996
, pp. 86
–99
.17.
Guckenheimer, J., and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, NY, 1983.
18.
Jiang, T., and Schellin, T. E., “Motion Prediction of a Single Point Moored Tanker Subjected to Current, Wind and Waves,” Proceedings of the ASME 7th International Conference on Offshore Mechanics and Arctic Engineering (OMAE’88), Vol. II, Houston, TX, February 1988, pp. 317–326.
19.
Kwan, C. T., and Bruen, F. J., “Mooring Line Dynamics: Comparison of Time Domain, Frequency Domain, and Quasi-Static Analyses,” Proceedings of the 23rd. Offshore Technology Conference, Houston, TX, May 1991, pp. 95–108.
20.
Lewis, E. V., ed., Principles of Naval Architecture, SNAME, Vol. III, Chap. IX, NJ, 1989.
21.
Martin
L. L.
Ship Maneuvering and Control in Wind
,” SNAME Transactions
, Vol. 88
, 1980
, pp. 257
–281
.22.
McKenna
H. A.
Wong
R. K.
Synthetic Fiber Rope, Properties and Calculations Relating to Mooring Systems
,” Deepwater Mooring and Drilling, ASME Ocean Engineering Division
, Vol. 7
, Dec. 1979
, pp. 189
–203
.23.
Oppenheim
B. W.
Wilson
P. A.
Low-Frequency Dynamics of Moored Vessels
,” Marine Technology
, Vol. 19
, No. 1
, Jan. 1982
, pp. 1
–22
.24.
Papoulias, F. A., and Bernitsas, M. M., “MOORLINE: A Program for Static Analysis of MOORing LINEs,” report to the University of Michigan/Sea Grant/Industry Consortium in Offshore Engineering, and Department of Naval Architecture and Marine Engineering, The University of Michigan, Ann Arbor, MI, Publication No. 309, May 1988.
25.
Papoulias
F. A.
Bernitsas
M. M.
Autonomous Oscillations, Bifurcations and Chaotic Response of Moored Vessels
,” Journal of Ship Research
, SNAME, Vol. 32
, No. 3
, Sept. 1988
, pp. 220
–228
.26.
Seydel, R., From Equilibrium to Chaos, Elsevier Science Publishing Co., Inc., New York, NY, 1988.
27.
Sharma, S. D., Jiang, T., and Schellin, T. E., “Dynamic Instability and Chaotic Motions of a Single Point Moored Tanker,” Proceedings of the 17th ONR Symposium on Naval Hydrodynamics, The Hague, Holland, Aug. 1988, pp. 543–562.
28.
Strandhagen
A. G.
Schoenherr
K. E.
Kobayashi
F. M.
The Stability on Course of Towed Ships
,” SNAME Transactions
, Vol. 58
, 1950
, pp. 32
–66
.29.
Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, NY, 1990.
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