悬链线型斜拉索风雨激振模型及特性分析

斜拉索长度随斜拉桥跨度增大而增长，以抛物线型近似代替实际状态下拉索线型的误差也越来越大。考虑水线与拉索表面之间存在库仑阻尼力和黏滞线性阻尼力，建立了基于悬链线型考虑面内-外耦合振动的运动水线连续弹性拉索风雨激振理论模型，并推导出以各阶模态为坐标的拉索振动微分方程。以不同参数拉索为例，对拉索与水线的耦合运动微分方程组进行数值求解，并将计算结果与基于抛物线型的拉索风雨激振理论模型进行了比较。结果表明：在某些情况下，拉索采用悬链线型与抛物线型的计算结果在拉索振幅、参振模态、空间振动形态、振动频率、拉索与水线相位差以及水线的振动频率上有很大差异；垂度影响系数对拉索低阶模态有较大影响，抛物线型垂度影响系数大约是悬链线型的一半；采用悬链线型建立的拉索风雨激振理论模型得到的拉索各阶模态的自振频率比采用抛物线型模型的计算结果要高，模态阶数越低，自振频率差距越明显。

Wind-rain-induced Vibration Model and Characteristic Analysis of Catenary Type Stay Cable

As the span of a cable-stayed bridge increases, the lengths of the cable also increase, and the errors associated with replacing the cable shapes with parabolic shapes also increase. In this study, the Coulomb and viscous linear damping forces between the cable and the rivulet surface were taken into account, and a theoretical model of wind-rain-induced vibration of the cable was established based on the static linearity of the catenary line considering the in-plane and out-of-plane coupling vibrations; further, the differential equation of cable vibration for each mode was derived in the form of coordinates. Taking different cable parameters as examples, the coupled differential equations of the cable and rivulets were numerically solved, and the calculated results were compared with those form the parabolic cable wind-rain-induced vibration theory model. The results show that the calculation results of cables using catenary and parabolic lines vary in amplitude, cable vibration modal, vibration frequency and space vibration form, phase difference between the cable and rivulet, and vibration frequency of rivulet. The influence coefficient of the sag has great influence on the low order mode of the cable, and the effect coefficient of parabolic sag is approximately half that of the catenary. The natural vibration frequency of each mode of the cable obtained from the theoretical model of the rain-wind-induced vibration established by the catenary lines is higher than that obtained from the parabolic model.