Bifurcations and Subharmonics in Stochastic Nonlinear Rolling

In this paper, the rolling motion of a ship is investigated to highlight the possibilities of falling in a bifurcation-and-jump scenario in a stochastic sea. It results that this possibility, while being remote in the typical standard sea spectrum, has a non negligible probability passing to narrow band excitation. This can be connected with local fluctuations or wave grouping in the wave record in beam sea and can give rise to bifurcations both in synchronism and in the first subharmonic due to the high degree of nonlinearity presented by the rolling motion. In following or quartering seas, the bifurcations reveal in terms of parametric resonance and are connected with the double effect of the advancing speed having as a result a reduction of centerpeak frequency and a hardening of the spectrum.