Effect of roll modelling in beam waves under multi-frequency excitation

This paper describes and compares three 1-DOF models for the description of roll dynamics in beam waves. Two models have a nonlinear restoring, while the third model is a linear model in restoring. All models are characterised by nonlinear damping. The two nonlinear models are different in the way restoring and excitation terms are implemented. One nonlinear model is based on a relative angle approach which incorporates the wave excitation into the ship roll restoring. The second nonlinear model is based on an absolute angle approach which separates the nonlinear restoring from the forcing term. Simulation results according to the three models are compared under two types of wave excitations: bi-frequency excitation and excitation generated according to specified sea spectra. The behaviour of the considered models is shown to be significantly different in some cases if nonlinearities of restoring are large. In particular, the restoring nonlinearities in the relative angle modelling introduce mixing frequencies effects which seem to be able to promote roll motion at resonance also when the excitation frequency is far from the roll natural frequency if roll restoring nonlinearities are sufficiently large.