Bridge J.

The vibration of nearly periodic structures has been studied extensively over the past two decades. While much of the emphasis has been on linear systems, some researchers have investigated the effect of nonlinearities on the form of the localisation occurring. In this work, the dynamic behaviour of a pair of parallel cables, continuously coupled by elastic strings, is investigated. Linear normal mode analysis shows that the system dynamics become localised if there is weak linear coupling and the cables are slightly mistuned i.e. they have minor differences in the individual system parameters. The emphasis of this work is to investigate localisation effects when the coupling is nonlinear. The nonlinear normal modes for the system are obtained in terms of amplitude, mode shape and frequency - the latter two being dependent on the amplitude and the total phase. The conditions leading to mode localisation are then analysed.