Analysis On The Chaos Behavior Of Vibration Of Stay-cable

As an important structural component of the stay-cable bridge, stay-cable under the rain or vehicle loads, it is prone to substantial vibration. Due to the mass, damping and stiffness of the stay-cable are relatively small. And with the span of stay-cable bridge constantly increasing, the vibration problem of stay-cable is getting more significant. Long time and large amplitude vibration of stay-cable has an effect on the durability of structure, which has become a severe issue in the development and operation of stay-cable bridge. The vibration of the cable will not only cause structural fatigue, resulting in the destruction of the anchorage side fatigue protection system, while the induced cable corrosion and even failure, in turn will shorten the service life of cables, so will affect the normal use of the bridge performance, and is easy for pedestrians to generate panic. In order to ensure the normal safe operation of the bridge and to ensure that the service life of the cable, it is necessary to study the static and dynamic characteristics of cable, and then provide a foundation for chaotic behavior of a Smale horseshoe sense. The following aspects of the work are involved in this paper:In the first place, we derive a stay-cable catenary formula, and on this basis, the static and dynamic differential equation of stay-cable is derived, and makes use of Galerkin method to decouple the dynamic equation of cable, so much so that we can get a set of ordinary differential equations.In the second place, using the Melnikov method, we can deduce the occurrence of chaotic conditions of stay-cable in the sense of Smale horseshoe. And then we can obtain the chaos threshold formula of homoclinic and heteroclinic orbits, so that lay a foundation for the further study of the chaotic movement of the stay-cable.In the last place, the Markov pation of Poincare mapping on single-mode vibration of stay-cable is dicussed, and its corresponding symbolic dynamical system is obtained. Laid the foundation for the further classification of a variety of complex motion orbits (including periodic orbits, quasi-periodic orbits, chaotic orbits, etc.) on stay cable utilizing the symbolic dynamics method.