Application of a three-dimensional aeroelastic model to study the wind-induced response of bridge stay cables in unsteady wind conditions

Abstract

The possibility of bridge stay cables experiencing violent dry inclined cable galloping raises great concern in the engineering community. Numerous experimental and analytical studies have been conducted to investigate this phenomenon, most of which were in the context of steady wind past a rigid cylindrical body. Real stay cables however, are generally long and flexible. They are exposed to more “broad” range of atmospheric boundary layer type of wind velocity profile which is also unsteady and turbulent by nature. To better understand the physics underlying this type of wind-induced cable vibration and to elucidate various contributing factors, a more realistic analytical model which is capable of addressing the above elements is imperative. In the current paper, a three-dimensional aeroelastic model is proposed to study the aerodynamic response of an inclined and/or yawed slender flexible cylindrical body subjected to unsteady mean wind, with practical application to wind-induced vibrations of bridge stay cables under no precipitation condition. The non-linear aerodynamic forces derived in the present study are combined with the cable free vibration equations available in literature to obtain the equations of motion for the wind-induced vibration of stay cables, which are solved numerically by an explicit finite difference scheme. The proposed three-dimensional aeroelastic model and numerical solution technique are validated by comparing the predicted cable free vibration responses with existing data in the literature. The mechanism which triggers dry inclined cable galloping and the required conditions for its growth are explored. In addition, the impact of different initial conditions and various unsteady mean wind scenarios on this violent cable motion are investigated. Results show that the occurrence of dry inclined cable galloping is associated with an opposite-phase relation between the relative wind speed and the aerodynamic force along the direction of cable motion in the critical flow regime. The cable would respond most violently should it be exposed to uniformly distributed steady wind in the critical Reynolds number range for a sufficiently long duration. The presence of multi-mode oscillation in a cable prior to its exposure to the critical flow condition would lead to a considerable reduction in cable response. Furthermore, the boundary layer type velocity profile would have a sizable impact on the cable aerodynamic response provided only a portion of the cable is subjected to the critical flow condition, and the unsteadiness in wind is found to have a stabilizing effect on cable aerodynamic response.