de Souza Junior, Jesse D'Assuncao Rebello; (1995) Geometrical methods of nonlinear dynamics in ship capsize. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

After centuries of designing and building ships, understanding the dynamic behaviour of marine vessels in severe seas is a difficult problem that still challenges naval architects. Capsize in rough weather does occur regularly, perhaps because of this lack of understanding of dynamic stability. The many accomplishments in the field of mathematical modelling of large-amplitude ship motions still have to be matched by corresponding achievements in the understanding of the dynamics of those models. We investigate in this work the essential features of current ship stability criteria, as well as the mathematical modelling of large-amplitude ship motions. Here we develop our own model of coupled heave-roll motions, in which both direct and internal parametric resonances are present. We then review the most relevant aspects of geometrical nonlinear dynamics with emphasis on some of the concepts and methods used to investigate the complex nonlinear phenomena related to ship capsize; attractor-following techniques, and bifurcation diagrams, transient and steady-state basin erosion phenomena, and integrity diagrams. Finally, we show how this approach, based on theoretical and numerical studies, can lead to a simple yet robust method to evaluate the dynamic stability of ships. Here we base our results on key observations about the nature and features of the processes of erosion and loss of transient safe basins. Through the use of coarse grids of starting conditions the method allows the construction of boundaries of safe motion in the space of phase variables and parameters. The predictions of this method can be easily checked against the results of low-cost experiments with physical models. With this work we hope to have contributed to the ongoing efforts to understand the complex nonlinear phenomena governing large-amplitude ship motions and capsize, and to have showed that such knowledge can be applied in the development of future practical methods of assessing ship stability.

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