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.