A Study on the Combination Resonance Response of a Classic Spar Platform

Abstract

The sum type combination resonance response of a classic spar platform is studied under a long periodic regular wave in this paper. The nonlinear differential equations for heave and pitch are established considering the time-varying incident wave elevation which is regarded as a parametric excitation. The first order steady-state response is solved by the method of multiple scales when the incident wave frequency approaches the sum of heave natural frequency and pitch natural frequency. The heave and pitch responses of a practical spar platform are obtained by solving the bifurcation equation using a numerical method. It is observed that the large amplitude sub-harmonic motion of heave and pitch mode are tripped when the wave height exceeds a certain value. The result shows that the spar platform may exhibit complicated dynamic behaviors when the sum type combination resonance occurs and indicates that the available damping plays a very important role in suppressing the instable motion responses.

Keywords

Classic spar platform parametric excitation sub-harmonic motion sum type combination resonance.

Get full access to this article

View all access options for this article.

References

Cavaleri, L. and Mollo-Christensen, E. , 1981, "Wave response of a spar buoy with and without a damping plate," Journal of Ocean Engineering 8(1), 7-24.

Choi, H.S. , 2006, "The motion characteristics of spar platforms of 3 generations," International Forum on Systems and Mechatronics .

Haslum, H.A. and Faltinsen, O.M. , 1999, "Alternative shape of spar platforms for use in hostile areas," in Proceedings of the 31st Offshore Technology Conference, Houston, TX, May 3-6, Vol. 2.

Hong, Y.P. , Lee, D.Y. , and Choi, Y.H. , 2005, "An experimental study on the extreme motion responses of a SPAR platform in the heave resonant waves," in Proceedings of the 15th International Offshore and Polar Engineering Conference , Seoul, Korea, June 19-24, pp. 225-232.

Koo, B.J. , Kim, M.H. , and Randall, R.E. , 2004, "Mathieu instability of spar platform with mooring and risers," Journal of Ocean Engineering 31(17-18), 2175-2208.

Nayfeh, A.H. , Mook, D.T. , and Marshall, L.R. , 1973, "Nonlinear couple of pitch and roll modes in ship motions ," Journal of Hydronautics 7(4), 145-152.

Ran, Z. , Kim, M.H. , and Zhen, W. , 1998, "Coupled dynamic analysis of a moored spar in random waves and current (time-domain vs frequency-domain analysis)," in Proceedings of 17th International Offshore Mechanics and Arctic Engineering Conference, Lisbon, Portugal, July 5-8, Vol. 121, pp. 194-200.

Rho, J.B. , Choi, H.S. , and Lee, W.C. , 2002, "Heave and pitch motion of a spar platform with damping plate," in Proceedings of the 12th International Offshore and Polar Engineering Conference, Kitakyshu, Japan, May 26-31, Vol. 12, pp. 198-201.

Rho, J.B. , Choi, H.S. , and Lee, W.C. , 2003, "An experimental study for mooring effects on the stability of spar platform," in Proceedings of the 13th International Offshore and Polar Engineering Conference, Honolulu, HI , May 25-30, pp. 285-288.

10.

Rho, J.B. , Choi, H.S. , and Lee, W.C. , 2004, "Vertical motion characteristics of truss spars in waves," in Proceedings of the 14th International Offshore and Polar Engineering Conference, Toulon, France, May 23-28, pp. 662-665.

11.

Rijken, O.R. and Niedzwecki, J.M. , 1996, "Dynamic response and run up on spar platforms," in Proceedings of the 6th International Offshore and Polar Engineering Conference, Los Angeles, CA, May 26-31, Vol. 1, pp. 289-295.

12.

Tahar, A. , Ran, Z. , and Kim, M.H. , 2002, "Hull/mooring/riser coupled spar motion analysis with buoyancy can effect," in Proceedings of the 12th International Offshore and Polar Engineering Conference, Kitakyshu, Japan, May 26-31, Vol. 12, pp. 223-230.

13.

Zhang, F. , Yang, J.M. , and Li, R.P. , 2007, "Numerical study on the hydrodynamic behavior of a new cell-truss spar platform," in Proceedings of the 26th International Conference on Offshore Mechanics and Arctic Engineering , San Diego, CA, June 10-15, Vol. 1, pp. 93-102.

14.

Zhang, F. , Yang, J.M. , and Li, R.P. , 2008, "Coupling effects for cell-truss spar platform: comparison of frequency domain and time domain analyses with model tests," Journal of Hydrodynamics 4(20), 7-24.