Non-linearity, bifurcation and chaos in the finite dynamics of different cable models

The finite dynamics of a suspended cable are discussed as a possible archetypal picture of the rich non-linear and chaotic behaviour occurring in the important class of elastic structural systems with initial curvature. The problem is attacked from different viewpoints concerned with both the modelization and the solution approach. A single degree-of-freedom model retaining some of the main features of the original system is first studied through numerical and geometrical techniques to obtain deep insight into the global behaviour. Attention is mostly devoted to some of the sudden bifurcation mechanisms of chaotic attractors. The requirements for a richer mathematical model of an elastic cable able to account for actual 3D dynamics are suggested by the results of experimental investigations on a suspended cable-mass model undergoing vertical support motion under various resonance conditions. Strong phenomena of multimodal interaction and chaos are presented. Finally, the onset of non-regular motions in a four degree-of-freedom theoretical model of a continuous cable is discussed either starting from the amplitude and phase modulation equations of an asymptotic solution, or based on direct numerical integrations of the ordinary equations of motion.