Design of a non-linear wire-rope tuned mass damper – linearized model-based approach

Wire rope springs are used in tuned mass damper applications due to their inherent energy dissipation properties, low cost, thermal stability and mechanical robustness. The dynamics of the wire rope springs are characterized by the relative sliding of the strands inside the wire ropes. Damping of the wire rope consists of the friction loss between the wire strands and structural damping under mechanical deformations. Moreover, the relative sliding alters the effective stiffness of the structure. These properties are non-linear and depend on the vibration amplitude. Modeling these non-linear dynamics has proven difficult, and no clear standard approach for design exist. In this paper, an amplitude based linearization framework is used to model the system dynamics for wire rope based tuned mass damper. The vibration suppression performance of the wire-rope tuned mass damper is compared to a linear tuned mass damper with similar mass ratio. The performance of the two dampers are compared for a system with multiple degrees of freedom, and the possible mistuning of the dampers is also considered. The results show that wire rope based tune mass damper, in comparison to a conventional linear tuned-mass damper, can suppress vibrations with a wider frequency band and under varying natural frequencies.