Two-degree-of-freedom inclined cable galloping—Part 1: General formulation and solution for perfectly tuned system

Galloping of inclined cables and other slender structures can occur in the critical Reynolds number range and/or in skew winds due to associated changes in the static force coefficients, even for cross-sections that are otherwise stable. A complete model of the quasi-steady aerodynamic forces leading to galloping has therefore been developed, for vibrations of any cylinder in two translatory degrees of freedom. It allows for arbitrary orientations of the flow velocity and the undamped vibration plane axes relative to the cylinder, and for variation of the force coefficients with Reynolds number and the relative angles. Analytical treatment of the eigenvalue problem has then led to an explicit expression for the minimum structural damping ratio required to prevent galloping for a perfectly tuned two-degree-of-freedom system, which it has been shown can differ significantly from the damping requirement for single-degree-of-freedom motion.     

Experimental study on the wind-induced vibration of a dry inclined cable—Part I: Phenomena

Besides rain-wind-induced vibration, field observations and a few experimental studies in recent years show that inclined cables also manifest wind-induced instability under condition when there is no precipitation. In order to further investigate these types of motion, including the limited-amplitude high-speed vortex excitations identified recently, experimental investigations were carried out. The focus of the present paper is on describing the dynamic and static model wind tunnel tests conducted and discussing the differences between divergent galloping motion and high-speed vortex excitation. Results show that the characteristics of dynamic responses and aerodynamic forces of these two types of motion are different. The former could be explained by a mechanism similar to that of classical galloping, whereas the latter might be related to vortex formation along the cable. The issues that require further investigation are also discussed.     

Experimental study on the wind-induced vibration of a dry inclined cable—Part II: Proposed mechanisms

The possibility of dry inclined cable galloping is of concern in the design of bridge stay cables. Although the phenomenon has only been observed in a few experimental studies, the fact that the mechanism of excitation is not fully understood makes it difficult to develop solutions with confidence. To clarify its physical nature, a series of dynamic and static model wind tunnel tests have been carried out in the current study. The present paper will focus on exploring the applicability of Den Hartog criterion and on an explanation of its driving mechanism. The spatial structure of the flow field surrounding an inclined cable will be examined to assist in better understanding of the phenomenon. Results show that the critical onset condition of the divergent motion predicted by the Den Hartog criterion (as applied to an inclined circular cylinder) agrees well with the experimental observation. However, satisfaction of the criterion only occurs within a critical range of Reynolds number. Further, within the critical ranges of wind speed and cable orientation, flow around the cable is found to be better organized. The resultant fluid forces acting at different longitudinal locations of the cable tend to point toward the same direction which generates greater cross-flow excitation force, and the axis-wise lift correlation is enhanced.