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Zbl 0969.70019
Jiang, C.; Troesch, A.W.; Shaw, S.W.
Capsize criteria for ship models with memory-dependent hydrodynamics and random excitation. (English)
[J] Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 358, No.1771, 1761-1791 (2000). ISSN 1364-503X; ISSN 1471-2962/e

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.

MSC 2000:: *70L05 Random vibrations (general mechanics)
70K50 Transition to stochasticity (general mechanics)
37N05 Dynamical systems in classical and celestial mechanics
76B20 Ship waves

Keywords: critical wave height; nonlinear random processes; global stability; large-amplitude rolling; capsize dynamics; frequency-dependent effect; dissipation of energy; history-dependent term; Melnikov function; phase-space transport techniques

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Zentralblatt MATH Berlin [Germany]