An Approximate Analysis On Nonlinear Ship Rolling

When ships navigate in waves, there will be large amplitude rolling which contains complex nonlinear phenomena. The serious nonlinear rolling, acted by outside forces or other factors, will lead ships to capsizing. In this paper, an approximate analysis of nonlinear ship rolling in still water and in waves by multiscale method was studied.Firstly, mathematical expressions of nonlinear damping and nonlinear righting moment were discussed, and the equations for nonlinear rolling motions in still water and in waves were established. Secondly, when the damping and the righting moment are separately nonlinear, and when both are nonlinear, the nonlinear ship rollings in still water were investigated by multiscale method and the 2nd-order approximate solutions were obtained. In comparison with linear rolling in still water, the effects of nonlinear damping and righting moment on ship's rolling motions were analyzed. Moreover, the multiscale method was used to study the main, ultraharmonic and subharmonic resonances of nonlinear rolling in waves, and the approximate solutions of the three resonances were given. At the same time, the characteristics of the three frequency-amplitude responses were analyzed depending on the secular terms. Finally, the nonlinear rolling were simulated by Runge-Kutta method. The results showed that the approximate analysis solutions were valid.