The random jumping of ship rolling in narrowband wave considering the static effect of liquid on board

Abstract

The random jumping of ship rolling excited by the narrowband waves is studied by the joint probability density function and the time history of the roll response, and the static effects of liquid on board is considered in this paper. The improved righting arm model is established including the angle of loll due to the liquid on board and the angle of vanishing stability. The narrowband input of the relative wave excitation moment is produced by means of linear filter action on the white noise. The four-dimensional Ito stochastic differential equation is numerically solved by the path integral method and the evolution of the joint probability density functions in the time domain is obtained. It is found that the ship rolling has two attraction regions when considering the effect of liquid on board. For the lower sea state, the joint probability density function trends to one peak and the ship rolls within one attraction region. For the higher sea state, the joint probability density function trends to two peaks, ship rolling jumps randomly from one attraction region to another, and the jumping frequency increases with the increase of wave exciting intensity.