Nonlinear parametric rolling in regular Waves - a general procedure for the analytical approximation of the GZ curve and its use in time domain simulations

A general procedure for the analytical approximation of the restoring arm in regular longitudinal waves is presented. The aim of the approximation is to obtain an analytical and accurate means for substituting the look-up table method in time domain simulations of realistic nonlinear parametric roll. The model is based on a 1.5-DOF system: the roll motion is modelled dynamically using a single degree of freedom, whereas the additional half DOF indicates that the coupling with heave and pitch is taken into account by means of hydrostatic calculations without considering dynamic effects. An analysis of the accuracy of the analytical approach is carried out taking into consideration different aspects of the problem (time histories, domains of attraction, chaotic behaviour, etc.). All the simulations are performed using data obtained from a real ship hull of a RoRo-Pax.