Frequency domain analysis of a tension leg platform with statistical linearization of the tendon restoring forces

The dynamics of a tension leg platform have important nonlinearities which must be approximated in some manner in a frequency domain analysis. For irregular waves, the well-documented method of statistical linearization is commonly employed for the drag forces, but it is seldom applied to the restoring forces. In earlier studies, the stiffness linearization has been limited to the surge motion. This paper presents the formulation for the linearization in all six degrees-of-freedom. To this end, the nonlinear restoring function and tangent stiffness matrix are derived, and extensive nonlinear couplings between the different modes are found to exist. The performance of the linearized frequency domain approach is benchmarked against time domain simulations for a problem involving large platform motions. It is found that subject to certain conditions, which are relatively mild, the linearization technique facilitates accurate predictions of the mean offsets and the response variances, including the slow-drift component.