Abstract
A method is proposed to deal with dynamic stability of ships in head seas based on a time-domain, non-linear numerical model of ship's motions in 5 degrees-of-freedom (sway, heave, roll, pitch, and yaw). A quasi-static approach is adopted for heave, roll, and pitch motions in waves, in which the calculation of significant variations on restoring coefficients is made using a pressure integration technique over the instantaneous submerged hull. Dynamic and hydrodynamic effects in waves for a given encounter frequency are included in the response calculations, which are based on a strip theory. Comparisons between numerical and experimental results demonstrated the adequacy of the technique proposed to predict parametric roll in regular waves. The results demonstrated also that the method is capable of predicting wave-induced parametric resonance not only in regular but also in irregular waves. Finally, in the stochastic excitation a certain threshold value is assumed for parametric roll response and then the probabilities of exceedance are calculated as a function of the prevailing weather and ship's operational conditions.