大跨度斜拉桥辅助索对索网系统面内自由振动特性的影响研究

Effect of Cross-ties on the In-plane Free Vibration Characteristics of Cable Network of Long-span Cable-stayed Bridges

大跨度斜拉桥斜拉索可通过辅助索连接形成索网系统,从而达到减振目的。为深入了解索网系统的真实动力行为,提高索网系统振动频率测试的准确性,以多层不等长索网系统为研究对象,通过理论推导建立索网系统平衡方程,借助MATHEMATICA对系统自振频率及振型进行求解,分析其面内自由振动特性;并使用数值模拟和试验方法对解析结果进行验证。此外,对多层不等长索网进行参数分析,包括辅助索刚度、辅助索位置、辅助索根数等,研究不同的辅助索设计方案对索网系统面内自由振动特性的影响。研究结果表明:索网系统内各根拉索的自振频率均相同;在整体振动的频率之间会出现局部振动或单根拉索单独振动的频率;施加辅助索会使目标索的基频增大;索网整体振动和局部振动的频率随着辅助索刚度减小而减小;随着辅助索根数增多,索网系统的基频逐渐增大;局部振动的振型出现得越晚,出现局部振动的最小频率越大。

Stay cables of long-span cable-stayed bridges are connected by cross-ties to form a cable network so as to control cable vibrations. In order to deeply understand the real dynamic behavior of the cable network and improve the accuracy of the vibration frequency test, this paper takes the multi-layer unequal length cable network as the research subject, establishes the balance equation of the cable network through theoretical derivation, solves the natural frequencies and modes of the system with the help of Mathematica, and analyzes the in-plane free vibration characteristics of the system. Numerical simulation and experimental methods are used to verify the analytical results. In addition, the parameters of multi-layer unequal length cable network are analyzed, including cross-tie stiffness, cross-tie position, cross-tie number, and the influences of different cross-tie design schemes on in-plane free vibration characteristics of the cable network are studied. The results show that the natural frequencies of all cables are the same;the frequencies of local vibration or single cable vibration will appear between the global vibration frequency;the fundamental frequency of the target cable will increase when the cross-tie is applied;as the stiffness of cross-tie decrease, the cable network’s frequencies of global vibration and local vibration decrease;with the increase of the number of cross-ties, the fundamental frequency of the cable network increases gradually;the later the local vibration mode appears, the greater the minimum frequency of local vibration appears.