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Capsize criteria for ship models with memory-dependent hydrodynamics and random excitation. (English) Zbl 0969.70019
Summary: The large-amplitude rolling and capsize dynamics of vessels in random beam seas are investigated using a nonlinear single-degree-of-freedom model. Included in this model are three types of damping moments -- the usual effects that are treated as linear and quadratic in the roll velocity, plus a frequency-dependent effect that captures the dissipation of energy caused by the generation of waves radiated away from the rolling vessel. The description of this type of damping requires a history-dependent term in the equations of motion. This memory effect prevents a straightforward application of the standard Melnikov method for determining capsize criteria. In this work, the Melnikov function and phase-space transport techniques are extended to derive a criterion for capsizing that can be applied to analytical models with this type of damping. Using these theoretical results, we obtain a closed-form asymptotic expression for a critical significant wave height, and this criterion is evaluated using simulation studies for a realistic set of vessel parameters.

70L05Random vibrations (general mechanics)
70K50Transition to stochasticity (general mechanics)
37N05Dynamical systems in classical and celestial mechanics
76B20Ship waves
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