HIGHLY NONLINEAR ROLLING MOTION OF BIASED SHIPS IN RANDOM BEAM SEAS

Recent developments in dynamical systems analysis are applied and exte nded to the study of highly nonlinear ship rolling motion and capsizin g in random beam seas. Damping and wave excitation moments are dealt w ith as perturbations since they are relatively small compared with ine rtial effects and hydrostatic righting moments. There is no restrictio n on the restoring moment due to hydrostatic loads, and bias effects a re included. Safe and unsafe areas are defined in the phase plane of t he unperturbed system model to distinguish the qualitatively different ship motions of capsize and noncapsize. Capsize events are represente d by solutions passing out of the safe region. The probability of such an occurrence is studied using the Melnikov function and the concept of phaseflux rates. Expressions for the phase space flux rate are deri ved and evaluated by numerical integration. The correlation of phase s pace flux and capsize is investigated through extensive simulation. It is shown that these analytical tools provide reliable, predictive inf ormation regarding the likelihood of a vessel capsize in a given sea s tate.