Nonlinear Analysis of the Dangerous Coupling Between Roll Motion and Vertical Motions in Head Sea

In this paper the possibility of excitation of parametric rolling on a ship advancing in head sea condition is studied on an experimental basis. The excitation of parametric rolling was effectively observed in the experimental tests, together with some case of capsizing. The parametric rolling exhibited the typical subharmonic behaviour. The use of classical Mathieu equation theory, coupled with hydrostatic calculations in longitudinal waves, accounting for both vertical motions and wave effect on stability, allows to explain in a very satisfactory way the observed phenomena. In addition, the problem of determination of roll damping dependence on ship speed was solved by using roll decay tests in calm water with forward speed. A simplified nonlinear modelling was proposed to account for the roll motion amplitude above threshold. The comparison with the experimental results is reasonably good