Prediction of the natural frequency of ship’s roll with regard to various models of roll damping

One of the most important dynamic phenomenon recognized as dangerous to seagoing ships is the resonance gain of rolling. This may occur due to nonlinearity of ship response in resonance conditions, i.e. when the encounter wave frequency is similar to the natural frequency of ship roll motion. Such coincidence should be avoided therefore shipmaster steers clear of some configurations of speed and course resulting in potential synchronous rolling. Nowadays, according to the IMO Intact Stability Code the natural period of roll is determined with the use of very simplified GM-based formula. The paper deals with the problem of more sophisticated prediction of ship’s natural rolling frequency with the use of the one degree-of-freedom roll equation with regard to nonlinear restoring moment. A special emphasis is put on the damping coefficient modelling which remains one of the crucial issues in terms of rolling simulation. Two typical approaches to the damping coefficient estimation are tested, the linear and the nonlinear one according to Ikead’s method. The set of ship roll simulations is carried out for a wide range of excitation frequency and a variety of exciting moment. The results of computation focused on the natural frequency of ship roll prediction are compared to assess the influence of damping model selection.