Numerical Method Research on Nonlinear Roll System of Large Container Ship

When dealing with the ship-roll problem, the roll motion is mainly regarded as a single degree-of-freedom dynamical system, and the nonlinear properties are reflected in the nonlinear damping term and restoring moment term. Previous studies have shown that transverse chaotic phenomenon means the damage of ship-roll stability which will lead to ship capsizing, and for ultra large container ships, the wind area above water surface can not be neglected, which turns the ship-roll system into asymmetric dynamical system. The concept of safe basin is usually used to express the boundedness of motion. It is defined as the set of bounded solution to dynamical system, and the erosion phenomenon of safe basin is normally explained as the global instability. This concept was firstly brought out by Thompson [1] when he studied the problem of ship capsizing and then was applied to different fields of engineering. Based on this background, the following three tasks are completed in this paper. a) For the calculation of chaos threshold, two numerical methods, namely, Pade approximation and Gauss-Legendre integration are adopted, analyzed and compared. b) One 9200TEU container ship is selected and the chaos threshold is calculated by virtue of Gauss-Legendre method. As numerical verification, the gradually erosion phenomenon of ship’s safe basin is observed and phase trajectories of points located in broken domain are traced; c) When encountered with crosswind (When winds are not parallel to or directly against the line of travel, the wind is said to have a crosswind component; that is, the force can be separated into two vector components, a crosswind component and a headwind or tailwind component.), the symmetry of ship-roll system begin to break. In the last part of this paper, the effect of crosswind on safe basin, asymmetry, and stability are studied.