Stochastic analysis of nonlinear coupled heave-pitch motion for the Truss Spar platform

Abstract

Considering the static stability and the change of the displacement volume, including the influences of higher order nonlinear terms and the instantaneous wave surface, the nonlinear coupled heave-pitch motion was established in stochastic waves. The responses of heave-pitch coupling motion for the Truss Spar platform were investigated. It was found that, when the characteristic frequency of a stochastic wave is close to the natural heave frequency, the large amplitude pitch motion is induced under the parametric-forced excitation, which is called the Mathieu instability. It was observed that the heave mode energy is transferred to pitch mode when the heave motion amplitude exceeds a certain extent. In addition, the probability of internal resonant heave-pitch motion is greatly reduced while the characteristic wave frequency is away from the natural heave frequency.

Keywords

Truss Spar platform / heave-pitch nonlinear coupling / stochastic waves / parametric-forced excitation / Mathieu instability

References

[1] Berthelsen PA (2000). Dynamic response analysis of a truss spar in waves. Master degree thesis, University of Newcastle.

[2] Basil T.P. Numerical simulation of the Truss Spar ‘Horn Mountain’ using couple, 2006, Texas: Texas A&M University

[3] Dong Y. Wave loads and response of the oil-extraction platform in deep ocean, 2005, Tianjin: Tianjin University Press

[4] Haslum HA, Faltinsen OM (1999). Alternative shape of Spar platforms for use in hostile areas. Proceedings of the 31st Offshore Technology Conference, Huston, 217–288.

[5] Holmes S., Bhat S., Beynet P. Heave plate design with computational fluid dynamics. Journal of Offshore Mechanics and Artic Engineering, 2001, 123(1): 22-28

[6] Hong YP, Lee DY, Choi YH (2005). An experimental study on the extreme motion responses of a spar platform in the heave resonant waves. Proceedings of the 15th International offshore and Polar Engineering Conference, Seoul, Korea, 19–24.

[7] Incecik A. Lecture notes: Wave forces on large diameter cylinder, 1999, Newcastle, UK: Department of Marine Technology, University of Newcastle

[8] Liu L., Tang Y. Unstability of coupled heave-pitch motions for spar platform. Journal of Ship Mechanics, 2009, 13(4): 551-556

[9] Rho JB, Choi HS (2002). Heave and pitch motions of a spar platform with damping plate. Proceedings of the 12th International offshore and Polar Engineering Conference, Kitakyushu, Japan, ISOPE, 198–201.

[10] Weggel D, Roesset J (1994). Vertical hydrodynamic forces on truncated cylinders. Proceedings of The Fourth International Offshore and Polar Engineering Conference, Osaka, Japan, 210–217.

[11] Yu Y. Random wave and its applications for engineering, 2000, Dalian: Dalian University of Technology Press

[12] Zhang L, Zou J, Huang EW (2002). Mathieu instability evaluation for DDCV/SPAR and TLP tendon design. Proceedings of the 11th Offshore Symposium. Society of Naval Architect and Marine Engineer(SNAME), Houston, 41–49.

[13] Zhao J., Tang Y. Nonlinear coupled responses of a classic spar platform in the heave resonant waves. Chinese Journal of Applied Mechanics, 2010, 27(1): 20-27