Sehmbi, Jatinder Singh; (2001) The dynamics of friction oscillators. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The aim of this thesis is to investigate the nonsmooth dynamical behaviour of a mechanical system, which undergoes self-sustained oscillations and chaotic motion induced by dry friction. Dry friction itself is not very easy to model and so a number of different models are investigated numerically. An experimental study is undertaken with a mechanical system which closely matches the mathematical system, to allow the formulation of the most physically realistic friction model for this system. It is shown that the complexity of the system can be increased by an appropriate increase in the dimension of the phase space of the system. The nonsmooth nature of the system and of its dynamical behaviour is further complicated by the fact that the phase space dimension varies. Thus classical methods of analysis are not especially applicable. To analyse the system new numerical techniques for determining Poincare maps and Lyapunov exponents are presented. The exploration of the multi-dimensional phase space of such a system would be difficult and computationally expensive. Therefore a method of reducing the complexity and dimension of the system to a lower dimensional map is presented. The different attractors of the system are found and bifurcation's of the system identified by use of the lower dimensional map. The significance of damping and external forcing on the system are investigated, as well as discussing the engineering considerations that they bring. Bifurcational behaviour of the system is then investigated using classical methods of analysis along with the computer program AUTO. A number of methods which prevent the stick-slip behaviour of the system are investigated with a view of eventually controlling the type of behaviour the system exhibits. A number of control methods are discussed and the application of an appropriate control mechanism for the system is presented.

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