The Stochastic Analysis of Slow Drift Motion

                                                               by Choi, Yong-Ho

                                     Abstract

     Slow drift motions are the result of nonlinear interaction effects between the 
irregular waves and the body motion. Since the damping of the mooring system is low,
large motions may occur. For moored floating offshore structures the slow drift motions
occur in surge, sway and yaw. Form the designer�fs point of view, slow drift motions are
very important.

     In this study, the responses are represented as a Volterra functional expansion of a
Nonlinear, time invariant system truncated after the second order term. Introducing
the linear and quadratic white noise with zero mean and unit variance, one can construct
eigenvalue problem to decide the coefficients of the linear and quadratic white noise. 
Then the mean upcrossing frequency is obtained by using the marginal and conditional
probability density function. The resulting expression for the mean upcrossing frequency 
is very complicated multiple integrals. Asymptotic expressions are adopted to get the 
closed form solutions for the extreme values.

     The numerical calculations are performed on a moored, floating cylinder. Newman�fs
approximation was calculated for the purpose of mutual comparison. The comparison shows 
that the Newman�fs approximation predicts larger responses than those calculated from 
proposed scheme.