Nonlinear Dynamic Response of Tension Leg Platforms

Summary

Scope of Work:
The use of time domain analysis for TLPs has increased in recent years due to the observation of the springing and ringing phenomena, associated with high frequency heave and pitch vibrations (at the corresponding natural frequencies) of a steady state and transient nature. The first objective of this work was to develop a comprehensive and thorough nonlinear dynamic analysis of several two-dimensional TLP models including all potential nonlinear effects. Morison’s equation (Morison et al., 1950) with several modifications allowing to include or neglect various sources of nonlinearities were implemented and used in the time domain dynamic analysis. A single cylinder, several cylinders and TLP hulls with and without pontoons were studied and subjected to regular and irregular waves. The models were floating or connected to the sea floor by tendons. The tendons were assumed to be massless elastic springs, allowing for time varying tension forces. The hydrodynamic forces on the tendons were neglected.

The nonlinearities investigated in this work are those associated with the following sources:

1. Wave kinematics:
   1. Different wave theories
   2. Consideration of convective accelerations
   3. Extending the wave kinematics up to the wave free surface and considering the variation of the wave free surface due to wave passage
2. Hydrodynamic forces
   1. Inclusion of the nonlinear viscous drag forces
   2. Implementation of the nonlinear modifications to Morison’s equation
   3. Inclusion of the wave-current interaction effect
3. Geometry of TLPs
   1. Variation of the TLP’s position with respect to the wave’s and hull’s motions
   2. Variation of the TLP’s position with respect to the wave’s and hull’s motions

The effects of the nonlinearities mentioned above on the slowly varying drift response (low frequency response) and the high frequency springing and ringing responses were studied. The time history and the corresponding spectral density, obtained using Fat Fourier Transform, for the motions of the three degrees of freedom (surge, heave and pitch) as well as for the tendon forces are presented. Selected results of the force components (e.g. inertia, drag, etc.) are also shown for some cases. In general, the time histories are used to study the motion and force amplitudes and mean values while their low and high frequency components are better observed in the spectral densities. The contributions of the low and high frequency response components of the TLPs to: the surge amplitude and mean drift and the limits (maximum and minimum) of the tendon forces, are evaluated. The relations between some of the structural and wave parameters are also investigated.

Also briefly described is the derivation of the first and second order wave theories with emphasis on their deep water simplifications and related free surface approximations. The procedure used to generate irregular waves and a brief discussion of some wave spectra is also included. The formulation of the models used in the study with their forcing functions are presented. The steps of the analyses and the description of all the options implemented in this work to isolate each nonlinear effect is included. The response of TLPs to regular waves is described and the effects of different nonlinearities on the low and high frequency response components are examined. The results of the TLP model subjected to irregular waves and their effects on the low and high frequency responses are examined.

Related Publications:
Johnson, C.P., Mekha, B.B., and Roesset, J.M. “Simplified Modeling for the Nonlinear Response of Tension Leg Platforms in Deep Water,” ISOPE-93, Third International Offshore and Polar Engineering Conference, Singapore, 1993.

Johnson, C.P., Mekha, B.B., and Roesset, J.M. “Effects of Different Wave Free Surface Approximations on the TLP Response in Deep Water,” ISOPE-94, 4th International Offshore and Polar Engineering Conference, Osaka, Japan, 1994.

Johnson, C.P., Mekha, B.B., and Roesset, J.M. “High Frequency Effects of the Modification to Morison’s Equation on the Response of a TLP,” 5th International Offshore and Polar Engineering Conference, The Hague, The Netherlands, June 11-16, 1995.

Pail, J.B., Mekha, B., Roesset, J.M. and Powers, E.J. “Interpretation of Nonlinear Effects on Dynamic Response of a TLP,” Proceedings of the 14th International Conference on Offshore Mechanics and Arctic Engineering, Copenhagen, Denmark, Vol.1, pp.199-206, June 1995.