Stay cables on several cable-stayed bridges all over the world have been found to experience rain-wind-induced vibrations under the combined action of rain and wind. Meanwhile, the bridge deck might also have obvious oscillation under the wind and/or traffic loads. The coupled responses of a stay cable under the combined rain–wind and support excitations are numerically investigated in this article. The equations of motion of a three-dimensional continuous stay cable are derived by considering the high-order nonlinear components of the dynamic cable tension, together with the equation of motion of the rivulet on the cable surface. The forces induced by rain–wind excitation are determined by the quasi-steady theory, and the support excitation is achieved by the boundary condition. The coupled equations of the cable and the rivulet are numerically solved by using the finite difference method and the fourth-order Runge–Kutta method, respectively. The numerical results show that the high-order nonlinear components of the dynamic cable tension should be taken into account to numerically reproduce the parametric vibration of the stay cable, whereas they hardly have any effects on the rain-wind-induced vibration and the resonance vibration of the stay cable. The responses of stay cable under vertical support oscillation only and the rain–wind excitation only obtained from this study agree well with the literature results. Compared with the results induced by single-source excitation, the cable response amplitude under the combined excitations is smaller than that induced only by support excitation and larger than that induced only by rain–wind excitation. The rivulet is prone to be thrown from the cable surface if the parametric vibration of the stay cable is evoked.

中文翻译：

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斜拉索在雨风和支座激励下的耦合响应理论分析

世界各地的多座斜拉桥上的斜拉索都被发现在雨和风的共同作用下经历了雨-风引起的振动。同时，桥面在风和/或交通荷载作用下也可能有明显的振荡。本文数值研究了斜拉索在雨-风和支撑激励联合作用下的耦合响应。通过考虑动态拉索张力的高阶非线性分量以及索表面上小溪的运动方程，推导出三维连续斜拉索的运动方程。雨-风激励引起的力由准稳态理论确定，支撑激励由边界条件实现。分别采用有限差分法和四阶Runge-Kutta法对缆索和河流的耦合方程进行了数值求解。数值结果表明，在数值再现斜拉索参数振动时，应考虑动索张力的高阶非线性分量，而对雨风致振动和共振振动几乎没有影响。的斜拉索。斜拉索仅在垂直支撑振荡下的响应和仅从本研究中获得的雨-风激励与文献结果非常吻合。与单源激发诱导的结果相比，联合激励下的电缆响应幅度小于仅由支撑激励引起的响应幅度，大于仅由雨-风激励引起的响应幅度。如果引起斜拉索的参数振动，小溪容易从索面抛出。