This project was initiated to investigate problems with the design and analysis of very-long span, highly flexible, bridges and in particular to examine the comparative stability and efficiency of various types of bridge for spans much longer than the present limit. The stability under wind loading of these structures is shown to be a primary problem. The various types of aeroelastic instabilities are presented; one class, vortex-shedding, is examined in more detail as it is not a problem for shorter structures but can be the cause of major problems for longer ones. It is shown that no existing analytical model for this behaviour is suitable. A new model is presented as an extension from an existing one-dimensional case so that it can describe the motion of a body in two directions. The new model is composed of two pairs of coupled non-linear differential equations; one for the structure and the other for the vortices. These must be applied at sections along the bridge span and over time. The new model was found to be a good method of comparing different types of bridge structure in a manner that has not previously been achieved. The model and its solution method were developed in a way that allowed additional damping methods, such as passive tuned mass dampers, to be included. The model is also able to include the effects of active control methods which vary in time. Models for both active mass dampers and active moving surfaces were developed. These were included in the bridge models to examine their effect on the behaviour of bridges at low wind speeds and to examine how such control methods could increase the ultimate stability of long flexible bridges. The solution methods of these equations were found to be numerically unstable in some circumstances and alternative strategies were investigated. A preliminary analysis was performed to investigate the stability behaviour of the solution method applied to the model equations. The work has shown the complexity of the behaviour of bridges under wind loading. Investigation of this behaviour has led to an understanding of the influence of the wind loads on the stability of structures and given insight into the design of new classes of longer (thus more wind sensitive) bridges. The new coupled--oscillator model allows the comparison of classes of bridge with various control mechanisms. This is in contrast to much of the literature which is specific to a single structure. The model could also be applied to other rectangular bodies in flow, for example bridge towers. The model has a much lower computational overhead and hence higher speed, by many orders of magnitude, than alternative computational strategies such as a combination of computational fluid dynamics and a structural finite element model. The project has brought together strands of information from the three distinct areas of bridge analysis, aeroelastic modelling and active control theory and combined them to investigate the behaviour of flexible structures under aeroelastic loading.
Keywords: Vortex-shedding, non-linear oscillator, active control, passive damping, long-span bridge.