Design guidelines for open-loop vibration control of stay cables using MR dampers

A mathematical model based on the complex modal theory is formulated to evaluate the damping ratio of cables incorporating smart magneto-rheological (MR) dampers in open-loop control mode, taking into account the damper coefficient, damper stiffness, damper mass, stiffness of the damper support, nonlinearity of the damper, as well as the cable sag and inclination. Based on asymptotic solution of the developed mathematical model, a 'generalized universal formula' is proposed to facilitate the damper design. Comprehensive parametric studies are carried out to analyze the effects on the maximum attainable damping ratio and the corresponding optimal damper coefficient. Making use of the 'generalized universal formula' and results from the parametric studies, design guidelines/procedures for open-loop cable vibration control using MR dampers are developed, for both single-mode optimal control and multi-mode suboptimal control. The guidelines/procedures facilitate the engineering application of MR dampers in mitigating the rain-wind-induced cable vibration on cable-stayed bridges.