Analysis of the galloping behaviour of an electrified railway overhead contact line using the non-linear finite element method

Galloping of an electrified railway overhead contact line (also known as catenary galloping) is a large-amplitude wind-induced vibration under extreme conditions that is extremely detrimental to the railway infrastructure. This paper attempts to conduct a numerical simulation of catenary galloping and analyse its galloping behaviour. Computational fluid dynamics is utilized to calculate the aerodynamic coefficients of the contact wire with different classes of wear. The mechanism of catenary galloping is revealed by the Den Hartog theory. To describe the non-linear behaviour of catenary galloping, a non-linear finite element method is employed to establish the catenary model, which properly considers the geometrical non-linearity of the contact/messenger wire and the non-smooth non-linearity of droppers. Considering the effect of fluid-induced vibration, the self-excited forces acting on the contact wire are derived. Through several numerical examples, the galloping responses of the catenary are analysed with different tension classes and stochastic wind. The results demonstrate that the extreme wear of the contact wire caused by the long-term passage of pantograph can change the aerodynamic coefficients of the cross-sections of the contact wire and cause the system's instability under steady wind load. It is concluded that upgrading the catenary tension class can effectively suppress catenary galloping. The stochastic wind only has small effect on the catenary galloping. The stochastic wind only has small effect on the catenary galloping.