Coupled responses of stay cables under the combined rain–wind and support excitations by theoretical analyses

Abstract

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.