Nonlinear coupled heave and roll oscillations of a ship in beam seas

The coupled (heave and roll) oscillations of a ship in transverse sinusoidal waves are considered. Extensive simulation studies show that resonance conditions may lead to large amplitude roll angles with the possibility of capsize. In contrast to much of the recent research in this area nonlinear effects, fluid-structure interaction and geometry of a realistic vessel are included in the analysis. The ship hull is described by a set of realistic transverse sections and fluid influence coefficients are computed using three-dimensional linear interpolation from tables taking into account the instantaneous waterplane and the frequency of the waves. The fundamental forcing parameters of this problem are the wave height and wave frequency. As expected, large response amplitudes occur for large wave height and proximity of the fundamental frequency of the waves to a natural frequency of the vessel. However, nonlinear effects have a strong influence on these results. Several initial conditions of the system were chosen and therefore transient effects are an integral part of this study. Combinations of wave parameters leading to either steady-state motion or capsize are mapped out as 'safe' and 'unsafe' conditions respectively.