Analysis Of Nonlinear Rolling And Stability Of A Ship In Waves

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 waves by multiscale method is studied, and use nonlinear dynamics method analyse the solution's stability.Firstly, mathematical expressions of nonlinear damping and nonlinear righting moment were discussed, and the equations for nonlinear rolling motions in waves were established. Secondly, when the damping and the righting moment are nonlinear, the method of multiple scales is used to determin a second-order approximate for the nonlinear harmonic responses. The pertubation solutions are compared with solutions obtained by numerical intergration of the nonlinear governing roll equation and the results show that the approximate analysis solutions are valid. A Floquet analysis is used to predict the stability of steady-state harmonic responses, and study the solution's jump, bifurcation and chaos phenomena. Mehiikov method was used to study the ship's nonlinear rolling differential equation, a numerical method was presented to compute the mehiikov function, and to get the curve of threshold above which chaos may occur. Finally, the LCEs(Lyapunov Characteristic Exponents) is employed in the field of chaotic detection for ship's nonlinear rolling system as the criteria for chaos.