Dynamic response of a compliant tower in wind and waves
Authors: Daneshvaran M.T.S. , Vickery B.J. 
Published: October 2008

ABSTRACT
The study of darnping was made using a surface piercing cylinder supported from a heavy three point pendulum system moving just above the water surface. The force are displacement time histories were recorded for a variety of free vibration damping tests, in still water, monochromatic and long crested random waves. The drag coefficient based on the relative velocity model was evaluated both from the damping traces and by matching of the measured and computed force time histories. Also in the course of the same experiment, the values of CM, CA were measured using the matching method for the range of Re, Ke numbers observed in the damping test. The results obtained from the above study were then employed to predict the response of the scaled model (1: 150) of a simple cantilever compliant tower to different wind/wave states in both frequency domain (linearized load) and stochastic time domain where the nonlinear drag force is considered in combination with the free surface effects. Finally the theoretical response is compared with the experimental results obtained in the wind/wave tank facility where the model was subjected to the combined action of the scaled random wave and wind loadings.

1 INTRODUCTION
The compliant tower is a slender jacket type structure which falls in the category of compliant platforms and is suited to deep water situations. Towers of this type resist the static loads through their stiffness while the first order wave loads are resisted primarily by inertia. Their typical first natural period due to the considerations on strength and stability is around 30 to 40 seconds. The second natural period is about 3 seconds so there would be little amplification of the response due to the first order waves. There is, however, dynamic amplification of the response due to the turbulent wind and free surface drag induced drift forces, and this response is significantly affected by the wave-motion induced drag damping.
The dynamic analysis of the compliant tower can be performed in time and frequency domains. In the former the nonlinearities associated with the system loading is considered, while in the latter the system and loading is linearized and the relation between the system response and applied loads, using principle of superposition, is given by a linear transfer function and the possible nonlinear loads would be expressed by higher order statistics. Significant effortsl-7 have been done to express the nonlinear force and developing computer based methods for rational stochastic, dynamic analysis of offshore platforms. However despite the considerable advances in analytical models that simulate the behaviour of offshore structures, experimental evaluation remains an alternative way to understand the physical aspects of the wave forces on slender structures and their response. For a semi-empirical model such as the relative velocity form of the Morison's equation in the case of structural oscillations in presence of waves, the quality of the response prediction depends on the accuracy of the experimentally determined force coefficients. Moe and Verley8 used the relative velocity model of the Morison equation to verify these force coefficients.