Stochastic Chaotic Roll Motion of Ship With Water on Deck

Abstract

The stochastic chaotic motion of ship rolling is studied considering the static effect of water on deck. The wave excitation is treated as periodic excitation perturbed by white noise and the parameter region for chaotic motion is determined by Melnikov mean-square criterion. The Poincare’ maps are constructed and the probability density functions are calculated using path integral method. It is found that the chaotic motion can be restrained by increasing ship damping and ship rolling response converges to two attraction regions. In the non-chaotic parameter region, ship rolls within one attraction region. In the chaotic parameter region the probability density function has two connected peaks and ship rolling jumps randomly from one attraction region to another.