Nonlinear Dynamic Analysis on the Rain-Wind-Induced Vibration of Cable Considering the Equilibrium Position of Rivulet

The nonlinear dynamic behavior of rain-wind-induced vibration of inclined cable is investigated with the consideration of the equilibrium position of the moving rivulet. The partial differential governing equations of three-degree-of-freedom on the model of rain-wind-induced cable vibration are established, which are proposed for describing the nonlinear interactions among the in-plane, out-of-plane vibration of the cable and the oscillation of the moving rivulet. The Galerkin method is applied to discretize the partial differential governing equations. The approximately analytic solution is obtained by using the method of averaging. The unique correspondence between the wind and the equilibrium position of the rivulet is ascertained. The presence of rivulet at certain positions on the surface of cable is then proved to be one of the trigger for wind-rain-induced cable vibration. The nonlinear dynamic phenomena of the inclined cable subjected to wind and rain turbulence are then studied by varying the parameters including mean wind velocity, Coulomb damping force, damping ratio, the span length, and the initial tension of the inclined cable on the model. The jump phenomenon is also observed which occurs when there are multiple solutions in the system.