Multi-modal nonlinear galloping in suspended cables: analytical and numerical approaches

The aeroelastic instability in quasi-steady regime (called “galloping” in technical language) is a classic phenomenon of aerodynamic instability of slender structures characterized by non-circular cross-sections. Typical structural systems susceptible to galloping are suspended cables subjected to icing conditions. In the technical literature the phenomenon is usually described by one degree-of-freedom models (mono-modal galloping). However, when the structure is in internal resonance conditions, more modes can be involved in the motion, thus originating a multi-modal galloping. The present paper was inspired by a geometrically nonlinear model of cable able to twist, recently proposed by the authors [1,2], which is a reformulation in the nonlinear range of a consistent linear model of curved cable-beam [3]. Considering a cable close to the first cross-over point, a multi-modal interaction occurs and it seems necessary to develop suitable analytical and numerical approaches. The aim of this paper is to verify the actual need of utilizing multi-modal models in galloping problems, and to check the qualitative and quantitative accuracy of the analytical perturbation solutions compared with numerical results.