斜拉桥动力学特性及涡激振动研究

发布时间：2018-05-25 05:24

本文选题：斜拉桥 + 涡激振动　；参考：《江苏大学》2017年硕士论文

【摘要】：由于斜拉桥具有较大的结构刚度、良好的结构性能以及外形美观等优势,在大跨度桥梁工程实践中具有很强的竞争力。同时,伴随着拉索新材料的引进和施工技术的快速发展,斜拉桥朝着更大跨度方向迈进,其结构也变得更加轻柔,自由振动和强迫振动等动力学问题也随之日益突出。因此,对斜拉桥固有特性进行分析是解决斜拉桥风、雨激振,地震及移动车辆等作用动力学行为的基础。作为一种在低风速作用时易发生的限幅振动现象,涡激振动过程中产生的较大振幅会影响行人与通车的舒适性,并引起结构的疲劳破坏。因此,对斜拉桥进行涡激振动研究,避免涡激振动的发生或将其振幅限制在一定的安全范围内,对桥梁工程实践而言具有极其重要的意义。本文回顾了桥梁风致振动研究背景与现状,以及涡激振动的发生机理与研究方法。通过采用连续体力学建模的方法,分别建立描述斜拉索、桥面和主塔动力学行为的偏微分方程,以及结构的边界与相容条件。在上述基础上建立斜拉桥结构的频率方程,求解频率方程得到固有频率,进而得到斜拉桥的振型函数。通过数值计算的方法分析主塔刚度系数对斜拉桥动力学特性的影响,并通过改变斜拉桥拉索长度和初始垂度等几何参数研究斜拉桥对称性破缺情况下可能发生的动力学行为。另外,本文还研究了一类单塔斜拉桥沿跨向受分布式涡激力作用时的振动响应情况。采用连续体动力学方法对斜拉桥进行建模,以Ehan-Scanlan模型为基础,引入分布式涡激力推导得到涡激振动方程。采用Galerkin法将斜拉桥控制方程离散为常微分方程组,运用Runge-Kutta法并借助于MATLAB软件求解斜拉桥涡激振动响应。通过数值算例研究并讨论了不同的初始构型下斜拉桥的涡激振动响应变化规律,探讨拉索非线性项对斜拉桥涡激振动响应影响,并比较了刚性塔模型与柔性塔模型所预测斜拉桥涡激振动响应的差异。最后,采用切换系统描述斜拉桥在模态跃迁与涡脱激振力联合作用时的动力学问题。以风速为分岔参数,结合时间历程图、相图等方法,分析模态跃迁下斜拉桥涡激振动响应的分岔行为。该研究可为斜拉桥的初始设计与振动控制提供理论依据。
[Abstract]:The cable-stayed bridge has the advantages of large structural stiffness, good structural performance and beautiful appearance, so it has a strong competitiveness in the practice of long-span bridge engineering. At the same time, with the introduction of new materials and the rapid development of construction technology, cable-stayed bridge is moving towards the direction of larger span, its structure becomes more gentle, and dynamic problems such as free vibration and forced vibration become increasingly prominent. Therefore, the analysis of the inherent characteristics of cable-stayed bridges is the basis for solving the dynamic behaviors of cable-stayed bridges such as wind, rain excitation, earthquake and moving vehicles. As a limiting vibration phenomenon which is easy to occur in low wind speed the large amplitude produced in the vortex-induced vibration will affect the comfort of pedestrians and traffic and cause fatigue damage of structures. Therefore, it is of great significance for bridge engineering practice to study the vortex-induced vibration of cable-stayed bridge to avoid the occurrence of vortex-induced vibration or to limit its amplitude to a certain safe range. In this paper, the background and present situation of wind-induced vibration of bridges are reviewed, and the mechanism and research methods of vortex-induced vibration are also discussed. By using the method of continuous mechanical modeling, the partial differential equations describing the dynamic behavior of cable, bridge deck and main tower, as well as the boundary and compatibility conditions of the structure, are established respectively. On the basis of the above, the frequency equation of cable-stayed bridge structure is established, and the natural frequency is obtained by solving the frequency equation, and then the modal function of cable-stayed bridge is obtained. The influence of the stiffness coefficient of the main tower on the dynamic characteristics of cable-stayed bridge is analyzed by numerical calculation, and the dynamic behavior of cable-stayed bridge under the condition of symmetry breaking is studied by changing the geometric parameters such as cable length and initial sag. In addition, the vibration response of a single tower cable-stayed bridge subjected to distributed vortex-induced forces along the span is also studied. The cable-stayed bridge is modeled by continuum dynamics. Based on the Ehan-Scanlan model, the vortex-induced vibration equation is derived by introducing the distributed vortex-induced force. The control equations of cable-stayed bridges are discretized into ordinary differential equations by Galerkin method. The vortex-induced vibration response of cable-stayed bridges is solved by Runge-Kutta method and MATLAB software. The variation of vortex-induced vibration response of cable-stayed bridge with different initial configurations is studied and discussed by numerical examples, and the influence of nonlinear term of cable on the vortex-induced vibration response of cable-stayed bridge is discussed. The difference between rigid tower model and flexible tower model in predicting the vortex-induced vibration response of cable-stayed bridge is compared. Finally, a switching system is used to describe the dynamic problems of cable-stayed bridges under the combined action of modal transition and vortex induced vibration. With wind speed as bifurcation parameter and time history diagram and phase diagram, the bifurcation behavior of vortex-induced vibration response of cable-stayed bridge under modal transition is analyzed. The research can provide theoretical basis for the initial design and vibration control of cable-stayed bridge.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：U448.27

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