Analysis of Motions of Semi-Submersible in Sea Waves
Authors: FuZhong Sun 
Published: October 2008

ABSTRACT
Starting from the analysis of the forces acting on a three dimensional cylinder with arbitrary symmetrical cross-section, taking account viscous effect and applying linear-processing technique, general expressions for the hydrodynamic forces, motion equation and its solution for semi-submersible platform in regular waves are given.
Based on linear theory of statistical analysis, it is proposed to employ the concept of "equivalent wave height" for the calculation of transfer functions with which both the short term and long term distribution and statistical characteristics of the motion of semi-submersible may be estimated. A computer program has been developed. Comparison between model experimental and theoretical data has shown satisfactory agreement.

INTRODUCTION
The motion behaviour and strength of semi-submersible had been investigated by many distinguished scholars, such as Hooft, l Kim, Chou, 2 Skoge, Pedersen3 The progress of research work has further improved the behaviour of semi-submersible drilling platform and has made many new types of semi-submersibles e.g. pipe layer, floating crane and multi-purpose platform into reality.
General speaking. the motion characteristics of semi-submersibles are very much better than ordinary surface vessels. However, for semi-submersibles which have to operate in long periods and under strictly restrained conditions, the motion behaviour is still a very important problem and the dynamic strength and stability are closely related to their motion behaviour.
Hooft's contribution enables one to calculate motion characteristics of semi-submersible in general. But for the semi-submersible which provided with two or three-dimensional non-circular cylinder it seems to be not adaptable, and the viscous damping quoted in (1) needs further investigation. Although the effect of viscous damping is not large for the motions in general, yet in resonance and some particular frequency range, such as zero potential exciting force range, the effect of viscous damping and viscous exciting forces will become important on the motion characteristics.
This paper starting from the analysis of the forces acting on a three dimensional cylinder with arbitrary symmetrical cross-section, general expressions for the hydrodynamic forces acting on a semisubmersible, either upright or in listed condition, are derived by taking the effect of viscous damping and viscous exciting forces and by employing principle of energy-equality to handle non-linear effect linearly. The concept of "equivalent wave height" is introduced for calculating transfer functions, with which both the short term and long term distribution and statistical characteristics of the motions of semisubmersible may be estimated. This proposed method is approximate for non-linear system in theory, but for the motions of semi-submersible in sea waves it is accurate enough for engineering purpose.

STATISTICAL ANALYSIS OF MOTIONS IN SEA
A fully developed sea may be considered as a stationary random process. When the atmospheric environment is changing, or when the sea is growing, both the sea and the motion of vessels will be unstationary in nature, however, if the period considered is short, it is reasonable to treat such unstationary phenomena as stationary random process. When the period is long, it is suggested to treat the sea waves and motions of platforms mathematically as a summation of a number of stationary random process.