Stochastic Modelling of Nonlinear Motions in the Presence of Narrow Band Excitation

For a nonlinear system described by a cubic nonlinearity of the righting moment in the presence of narrow band stochastic excitation, steady state motion variances are obtained by means of a perturbation scheme, both near synchronism and in correspondence to the first subharmonic. The results show the possibility of bifurcations in both regions, provided the excitation bandwidth is enough narrow. The results of a numerical simulation confirm this possibility. The differential equation analysed is typical of the description of first order motions of floating structures. The possibility of bifurcations, which represent a marked deviation from Gaussian behaviour, makes it necessary to reconsider the recently developed mild nonlinear/non-Gaussian stochastic modelling for the evaluation of hydrodynamic safety and fatigue life of structures.