Asymptotic expansion of ship capsizing in random sea waves—II. Second-order approximation

Abstract

This is a continuation of Part I [ Int. J. Non-Linear Mech. 30, 727–740 (1995)] on the first-passage problem of ship roll oscillations in a random sea. A new coordinate system based on the canonical action-angle variables is used to express ship roll motion in terms of a set of Ito stochastic differential equations. The Pontryagin equation which describes the mean exit time of the system is solved using the method of asymptotic expansion. In the present analysis, a second-order approximation is carried out. The solution includes the contribution of the boundary layer, which compensates for the residual in the boundary condition at the barrier. It is found that the second-order approximation solution yields better results and takes into account such effects as the mean value of the excitation and other additional non-linearities which were not accounted for in the first-order approximation.