Investigation of coupling between external and parametric resonances in small sagged inclined cables
Résumé
The coupling between parametric and external resonance of inclined stay-cables subjected to an imposed motion of their anchorage, having components both along the axis of the cable and perpendicular to the axis, will be investigated. An in depth state of the art review on multi-modal interactions of cables with moving anchorages will first be presented, with Rega's work playing a pivotal role in the investigation of this phenomenon. Then, an analytical model will be proposed, based on the harmonic balance method, which will be as simple as possible, but sufficient for the investigation of coupling between the first and second eigenmodes, i.e. between parametric and external resonances. Next, two specific cases of the general model, in which no coupling appears, will be studied, in order to identify the intrinsic characteristics of external and parametric resonance, respectively. Finally, the coupling of both instabilities will be investigated, aiming at a better understanding of the interaction phenomenon and at the definition of practical engineering guidelines in the form of conditions under which different types of response may be anticipated.
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