基于异步振动的桥面激励斜拉索辅助索减振理论与试验研究

With the increase of the span of cable-stayed bridges, cables become more and more slenderer and lighter which leads to more vulnerable to the excitations of wind (rain) and vehicle load. The damping effect of various dampers on extra-long cables is often not good, and the damping method of crosstie is not yet mature, thus, the vibration mitigation of long cables has becomes a key problem to be solved urgently. The previous studies show that good mitigation performance existing when the cable vibrations are asynchronous rather than synchronization one. Hereby, based on the stay cables under deck excitation, the nonlinear dynamics model of cable and cable-crosstie will be derived, and the nonlinear differential equations of motion and these approximate analyses, numerical calculations and experimental investigations will be performed via the statistical theory, nonlinear dynamics theory and modern testing techniques. The proposed project is expected to reveal the relationship among the cable vibration phase difference, cable parameter and excitation frequency so as to determine the parameter region of asynchronous vibration. The relationships among the affect parameters and the mitigation effect will be studied to reveal the vibration mitigation mechanism. An asynchronous-based crosstie vibration mitigation arrangement will be proposed. Corresponding experiments will be done to validate the approximate analyses and numerical results and also modify the obtained theoretical model. This project is of great theoretical significance and application prospect not only to enrich the understanding of the cable large amplitude vibration and collision and a type of vibration problem of adjacent structures (components) with similar parameters, but also lay the theoretical foundation and provide technical reserves for the vibration mitigation technology of long cables.

随着斜拉桥跨径的不断增大，斜拉索变得愈加细长和轻柔，在风（雨）、车辆等激励下更易发生大幅振动。各类阻尼器减振措施对特长拉索的减振效果往往不佳，而辅助索减振手段且尚不成熟，因此，长斜拉索减振问题已成为亟待解决的关键问题。研究表明：拉索振动“异步”则辅助索减振效果好，“同步”则效果差。据此，本项目将综合运用统计理论、非线性动力学理论和现代测试技术，以桥面激励下的斜拉索为研究对象，建立斜拉索非线性动力学模型和斜拉索-辅助索非线性动力学模型，推导运动微分方程，开展近似解析分析、数值分析和试验研究。项目预期将探明无辅助索时拉索振动相位差与拉索参数、桥面激励频率的匹配关系，确定“异步”振动参数域；探明各参数对辅助索减振效果的影响规律，揭示辅助索减振机理；提出基于“异步”振动的辅助索布置方式；通过模型试验，验证部分近似分析和数值计算结果，修正力学模型。项目研究成果将丰富对拉索大幅振动及其影响、拉索碰撞以及一类相邻布置的参数相近结构（构件）振动问题的认识，为发展特长拉索减振技术奠定理论基础并提供技术储备，具有重要科学意义和应用前景。

索结构振动控制一直是桥梁工程领域的热点问题，辅助索是长索振动控制中一种富有潜力的手段，但其减振效果与所连接的拉索参数差异密切相关，拉索振动“异步”则辅助索减振效果好，“同步”则效果差。本项目以拉索相频特性研究为起点，揭示相近参数拉索的同/异步振动机理，为辅助索减振技术提供理论基础。同时，对动力学方程的无量纲化处理进行研究，提出一种可将方程规范化至最简、最具一般性的方法，从而大大简化相关问题的研究工作。具体而言，本项目取得的研究成果及意义如下：（1）建立了考虑相位的两端三向激励索结构的无穷模态动力学模型，模型可退化至任意一种激励情况、模态激发情况或内共振情况，有利于研究索结构在多种激励下的复杂非线性动力学现象；（2）建立了M道辅助索连接N根垂索的垂索-辅助索一般动力学模型，得到了矩阵行列式的一般表达式，能退化到任意多辅助索-斜拉索的情况；（3）提出了一种普遍适用的动力学方程无量纲处理方法以将任何动力学方程化至最简、最具一般性的形式。以此为基础，提出了一种新的参数识别方法。这项研究大大简化了正/反问题的难度，为相关问题的研究打开了新的工作面；（4）研究了单索的瞬时相片特性，提出了可刻画瞬时相位差大小的参数。通过试验和理论分析揭示了同/异步振动的机理与辅助索减振的方式，为辅助索减振设计理论提供了理论支撑。