Highly nonlinear rolling motion leading to capsize

Extremely large amplitude ship rolling motion in random seas leading to capsize is investigated using the modern techniques of nonlinear dynamical systems analysis. Safe and unsafe areas are defined in the phase plane of the unforced undamped system to distinguish the qualitatively different ship motions of capsize and noncapsize. The occurrence of complex and qualitatively different dynamics is studied using the concept of phase space flux and its measurement via Melnikov functions. The correlation of phase space flux and capsize is demonstrated through extensive simulation of the system with random excitation.; Special techniques have been proposed to include the effects of bias, system memory, and couplings from other modes of motion. The differences and the relation of the rates of phase space flux between the unbiased and biased systems are addressed. Melnikov function and phase space flux analysis have also been shown to be viable for a time-variant system with a convolution integral representing the frequency dependency of the coefficients. The couplings from other modes are modeled as parametric excitations. Numerical schemes have been devised for simulation of the resulting integro-differential equation with parametric excitation in addition to external excitation.; The use of modern dynamic analysis methods provides a better understanding of the dynamic capsizing phenomenon and an efficient way to predict the initiation of capsize. The approaches developed in this thesis make it possible to study a sophisticated and realistic ship roll model using the modern geometric methods. Parameter comparison studies through phase space flux analysis can be used to improve ship design and operations.