| Popis: |
The paxametrically excited pendulum system is a dynamical system that can exhibit many nonlinear phenomena including that of chaos. Initially in this work, an examination of the symmetric parametrically driven system is undertaken and its bifurcational nature is highlighted in detail. In any physical representation of a mathematical model, perfect symmetry can never quite be achieved even with elaborate and detailed experimental arrangements. So, it is necessary to gain a deeper understanding on how breaking the symmetry of this specific system can affect its bifurcational and nonlinear behaviour. This work continues to examine this asymmetric case and perform a comparison with its symmetric counterpart, with the aim of providing a better physical realisation of the model. The experimental importance of undergoing such an alteration in a system is discussed and applications to field of ship dynamics are investigated. In addition, an examination of another form of the parametrically excited pendulum is considered where an extra harmonic forcing is incorporated within the equation of motion. The relevance of such an extension as well as of the study of the single parametrically excited system is shown by their proposed application to ship dynamics. Experimental roll decay tests are performed at the National Technical University of Athens, Greece, on a newly designed monohull model. Results are compared with corresponding adopted trimaran tests recently conducted by the Naval Architecture and Marine Engineering Research Group of UCL in conjunction with QinetiQ Haslar. The intention is to convey that by implementing equations of single and double forcing in the numerical simulations, better characterisation of the behaviour of roll damping assessment for these models is achieved, since adapting existing theoretical methods do not yield accurate roll damping predictions. Consequently, this attempt may develop a validated theory for the prediction of monohull and trimaran roll motion and furthermore results from this nonlinear study may provide a more useful approach for future analysis of multihull vessels. |
