The Effect of Eccentricity on the Nonlinear Galloping of Cables Considering Wind Flow and Support Motion in 1:1 Internal Resonance

Galloping of cables is a kind of self-excited vibration and characterized with high amplitude and low frequency vibration. In this paper for investigating the nonlinear galloping of an inclined cable, considering flexural and torsional stiffness, a cable-beam model is used. The iced cable is formulated under the effects of combined wind flow and support motion. Assuming low sag to span ratio and using physical parameter values of the cable, the governing equation of motion is obtained as a classical equations of the perfectly flexible cable, plus a further equation governing the twist motion. These two degrees of freedom system is discretized via the Galerkin method, by taking in-plane and out-of-plane modes as trial function. Two resulting non-homogeneous ordinary differential equations are coupled and contain quadratic and cubic nonlinearities in both velocity and displacement terms. By using multiple scale method for 1:1 internal resonance, a first order amplitude-phase modulation equation, governing the slow dynamic of the cable, is obtained. In this paper the wind speed and the eccentricity of the iced section are set as the control parameters. Without consideration the eccentricity, the value of amplitude is increased as the wind speed is increased. But considering the eccentricity is reduced to firstly increasing and then decreasing the amplitude.