On the Dynamic Response of Buoy-Supported Cables and Pipes to Currents and Waves
Authors: Hicks James B. , Clark Lyle G. 
Published: October 2008

Introduction
Several possible applications exist for a system characterized as a subsurface buoy supporting a slender column attached to the ocean floor. Such systems have been suggested as the basis for offshore loading and production facilities, flare towers, and drilling platforms. Drilling risers supported at the top by buoyant chambers fall in this category, and, if the "column" is perfectly flexible, we may also include subsurface buoys anchored by single cables in this class of systems. The so-called articulated drilling tower is an example in which the column would be fairly stiff.
Of essential interest in the design of such structures is their dynamic response to currents and waves and the resulting stresses induced by the motion. Many previous efforts have dealt with related systems. Among these we can cite work concerning drilling risers supported by surface ships or platforms, (5,6,7) and studies of cable-anchored buoys (1) Perhaps most applicable is the work discussed at this conference last year by Blazy, et.al., which treats the dynamics of the ELFOCEAN articulated platform(2). Generally, the mathematical models in these papers were limited by at least one of the following assumptions:The motion is two-dimensional.The deflections from some equilibrium position are small.The motion of the top of the column (or pipe or cable) is specified.
To the authors knowledge, no one has presented a model which includes the three-dimensional effects of cross currents (i.e., currents running obliquely to the direction of wave propagation), and which allows large deflections with the motion of the top dependent upon the interaction of the system and the water.
Because of the complex manner in which the system parameters inter act in determining the system's response, any mathematical model intended for use as a practical design tool should be as simple as possible. Otherwise, the computation time and expense necessary to determine useful design parameters may become excessive. Our objective was to develop a model which is consistent with these requirements, yet is sufficiently general to offer a wide range of applicability.
The primary restriction placed on the model presented here is that the bending stiffness must not significantly affect the gross motion of the system. The effects of tension are assumed to predominate. It is felt that this limitation is not unduly severe in most deep-water applications. Steady-state solutions for the motion obtained from the zero-stiffness model are used to determine local bending stresses due to column stiffness.

Mathematical Model
The following general assumptions are made concerning the system construction and behavior:The column is of uniform cross section with a length which is much larger than the diameter.Local deformation is small and linearly elastic, but the gross displacement of the column may be large and three-dimensional.The column is attached at the bottom either by a universal joint or by being rigidly built in, or by being elastically restrained from rotating.Column stiffness does not appreciably affect the structure motion.