【作者】 颜庆丽；

【导师】 李金海；

【作者基本信息】 大连理工大学 ， 建筑与土木工程， 2012， 硕士

【摘要】 斜拉索作为斜拉桥的重要的结构构件,在风雨或者车辆荷载的作用下,很容易发生大幅的振动。由于斜拉索的质量、阻尼以及刚度都比较小,而且随着斜拉桥跨径的不断加大,斜拉索的振动问题日臻显著。斜拉索长时间的大幅振动对结构耐久性的影响已成为斜拉桥发展和运营中的严峻课题。拉索的振动不仅会导致结构的疲劳,使得拉索锚固端的疲劳保护系统发生一定的破坏,同时导致拉索发生锈蚀甚至失效,进而会使拉索的使用寿命相应的减少,这样就会影响桥梁的正常使用性能的发挥,而且容易使行人产生恐慌心理。为了保证桥梁正常的安全运营以及确保拉索的使用寿命,有必要对拉索的静动力特性进行研究,进而为拉索发生斯梅尔马蹄意义下的混沌特性研究提供了一定的基础。本文主要完成了以下几个方面的工作：首先,推导出了斜拉索的悬链线公式,并且在此基础上,建立了斜拉索的静、动力微分方程,并且运用伽辽金方法对拉索的动力方程进行了解耦,得到了一组常微分方程。其次,运用梅尔尼科夫方法,推导出了斜拉索发生斯梅尔马蹄意义下的混沌的条件。进一步得出了同宿以及异宿轨道混沌的门槛值公式,为进一步研究斜拉索的混沌运动奠定了一定的基础。最后,讨论了斜拉索单模态振动的Poincare映射的马尔可夫分割性质,并找到其对应的符号动力系统,为进一步利用符号动力学方法将斜拉索的各种复杂运动轨道(包括周期轨道、拟周期轨道、混沌轨道等)进行分类研究奠定了基础。更多还原

【Abstract】 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.更多还原