Structural cables are rapidly diffusing in the modern civil engineering for their valuable static, economic and aesthetical performances. Among different countermeasures to protect them against dynamic sources of high amplitude oscillations, semi-active strategies presently represent a promising solution for field application in mitigating the vibrations of bridge stay cables. In the present paper an analytical model is formulated to describe the dynamics of a taut cable passively controlled by a transversal magnetorheological damper. The coupled dynamics of the cable-damper system is investigated, and different rheological models, with an increasing number of control parameters, are used to describe the damper force-displacement relationship. Focus is made on understanding the damper efficacy and the model reliability within different possible oscillations regimes observed during an experimental campaign of laboratory tests
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