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The application of nonlinear dynamics to ship roll and capsize

Cotton, Ben; (2000) The application of nonlinear dynamics to ship roll and capsize. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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In this thesis we study a single degree of freedom model for ship roll motion. We model roll motion as a forced oscillator in a nonlinear potential well. By considering capsize as escape from this potential well, we have been able to apply many of the techniques of nonlinear dynamics developed in recent years to predict and better understand this behaviour. It has been found in previous studies that bias in the restoring force for nonlinear oscillators can have a significant effect on the steady state solutions and, importantly for escape, reduce the region in which safe solutions exist. Using a parameterised family of restoring functions, the significance of bias for steady state solutions is investigated further. In particular we study the frequency dependence of such symmetry breaking and associate the observed behaviour with the bifurcations in parameter space. We then study some aspects of the application of Melnikov's method for the location of saddle connection orbits, which can cause a dramatic increase in the likelihood of transient motions leading to escape. Again we are interested in how this method should be applied to slightly biased systems. We then study the modelling of damping functions and how this can affect capsize. Using Melnikov's Method we develop a new concept of equivalent linear damping, specifically designed to model damping close to capsize amplitudes. We accompany this theoretical work with results from a series of large angle roll decay tests and the key features of damping at capsize amplitudes is discussed. The predictions from the theoretical work within this thesis and previous studies are then tested against capsize experiments conducted with a specially designed prismatic model. Here we are interested in how well the single degree of freedom roll model approximates real roll motion and capsize. Nonlinear features of the roll motion are observed and we also compare the experimental results with the approximate and numerically derived predictions for capsize. To conclude we discuss the possibilities for future application of these ideas and techniques within the field of ship design. An optimisation based approach to hull design is described and we ask what the next steps should be in the application of the nonlinear dynamical approach to ship capsize.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: The application of nonlinear dynamics to ship roll and capsize
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest.
Keywords: Applied sciences; Ship capsizing
URI: https://discovery.ucl.ac.uk/id/eprint/10120828
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