Occurrence of resonant roll motion due to multi-frequency off-resonance excitation: a preliminary numerical investigation

The paper addresses the roll behaviour of ships with significant restoring nonlinearities in beam waves. A simplified 1-DOF roll dynamical model based on a relative angle approach for the restoring term is described and employed. A more widely used model based on an absolute angle modelling for the nonlinear roll restoring, and a model with linear restoring are also considered in order to provide a ground for comparison. The relative angle modelling is qualitatively discussed to show the possibility that the frequency mixing induced by nonlinearities of restoring, which apply directly to the forcing, could create forcing terms falling close to the roll resonance frequency. Numerical simulations are performed for a hull with hardening restoring and relatively low metacentric heights. Two cases are considered in the simulations: an archetypal two-harmonics forcing and the case of irregular waves. In both cases it will be shown that nonlinearities of restoring are responsible for the creation of indirectly excited harmonic components of roll motion close to the roll natural frequency. Interesting additional nonlinear effects are highlighted, in particular in case of irregular sea excitation.