A recently developed approach, in the area of nonlinear oscillations, is used to analyze the single degree of freedom equation of motion of a oating unit (such as a ship) about a critical axis (such as roll). This method makes use of a closed form analytic solution, exact upto the rst order, and takes into account the the complete unperturbed (no damping or forcing) dynamics. Using this method very-large-amplitude nonlinear vessel motion in a random seaway can be analysed with techniques similar to those used to analyse nonlinear vessel motions in a regular (periodic) or random seaway. The practical result being that dynamic capsizing studies can be undertaken considering the shortterm irregularity of the design seaway. The capsize risk associated with operation in a given sea state can be evaluated during the design stage or when an operating area change is being considered. Moreover, this technique can also be used to guide physical model tests or computer simulation studies to focus on critical vessel and environmental conditions which may result in dangerously large motion amplitudes. Extensive comparitive results are included to demonstrate the practical usefulness of this approach. The results are in the form of solution orbits which lie in the stable or unstable manifolds and are then projected onto the phase plane.

Ship roll motion has been the subject of many studies, because of the complexities associated with this mode of ship motion, and its impact on operability, safety, and survivability. Estimation and prediction of the energy transfer and dissipation of the hydrodynamic components, added inertia and damping, is essential to accurately describe the roll motions of a ship. This is especially true for ship operations in moderate to extreme sea conditions. In these conditions, a complex process of energy transfer occurs, which alters the physical behavior of the hydrodynamic components, and ultimately affects the amplitude of ship roll motion. Bilge keels have been used on ships for nearly two centuries, to increase damping and reduce the severity of roll motions experienced by a ship in waves. Because ship motions are more severe in extreme sea conditions, large roll angles may occur. With the possibility of crew injury, cargo damage, or even capsize, it is important to understand the behavior of the roll added inertia and damping for these conditions. Dead ship conditions, where ships may experience excitation from beam, or near beam, seas present a worst case scenario in heavy weather. The behavior of a ship in this condition should be considered in both the design and assessment of seakeeping performance. In this study, hydrodynamic component models of roll added inertia and roll damping were examined and assessed to be unsuitable for accurate prediction of ship motions in heavy weather. A series of model experiments and numerical studies were carried out and analyzed to provide improved understanding of the essential physical phenomena which affect the hydrodynamic components and occur during large amplitude roll motion. These observations served to confirm the hypothesis that the existing models for roll added inertia and damping in large amplitude motions are not sufficient. The change in added inertia and damping behavior for large roll motion is largely due to the effects of hull form geometry, including the bilge keels and topside geometry, and their interactions with the free surface. Therefore, the changes in added inertia and damping must be considered in models to describe and predict roll motions in severe wave environments. Based on the observations and analysis from both experimental and numerical methods, several time-domain model formulations were proposed and examined to model hydrodynamic components of large amplitude roll motions. These time-domain formulations included an analytical model with memory effects, a piecewise formulation, and several possibilities for a bilge keel force model. Although a piecewise model for roll damping was proposed, which can improve the applicability of traditional formulations for roll damping to heavy weather conditions, a further attempt was undertaken to develop a more detailed model specifically for the bilge keel force. This model was based on the consideration of large amplitude effects on the hydrodynamic components of the bilge keel force. Both the piecewise and bilge keel force models have the possibility to enable improved accuracy of potential flow-based numerical prediction of ship roll motion in heavy weather. However, additional development remains to address issues for further practical implementation. / Ph. D.