| Summary: | As engineering structures become increasingly lightweight and flexible, their nonlinear dynamic behaviour becomes increasingly significant; however, such behaviour presents a number of challenges. For example, nonlinear system identification is often restricted to relatively simple structures, or to methods that provide limited physical insight, whilst features such as bifurcations and multiple solutions present numerous challenges for modelling and experimental testing. The aim of this thesis is to further the theoretical understanding of the behaviour of systems with smooth nonlinear characteristics, and provide practical insight into the significance of such behaviour. An analytical approach is employed throughout, providing an understanding of the relationship between the physical characteristics of a system, and the behaviour it exhibits. Backbone curve analysis is also utilised, which considers the equivalent unforced and undamped system to provide an interpretation of the underlying nonlinear dynamic behaviour. A number of novel behaviours are identified in a conceptually simple, two-mass oscillator, including out-of-unison and phase-varying backbone curves, the former of which is shown to be equivalent whirling motion in a cable. An analytical, energy-based technique is then introduced as a method for formulating a link between backbone curves and resonant forced responses. This is first demonstrated using a two-mass oscillator, before being applied to a nonlinear beam where it is used to predict the existence of an isola in the forced response. The concept of a general periodic motion in an undamped nonlinear system is then considered, and it is shown that two classes of backbone curve may exist: one where locking exists between the fundamental components of the motion, and one where only the harmonics exhibit locking. The mechanism behind locking is described via an extension of the aforementioned energy approach, and this is used to explain why motions that are locked in the harmonics are seldom observed. The theoretical understanding gained in this thesis is then used to develop a practical framework for nonlinear system identification, which draws upon the advantages of both the analytical method and the backbone curve analysis. Furthermore, the energy based approaches developed throughout are used to understand the limitations of the proposed identification framework, and provide insight into how these limitations may be overcome.
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