Theoretical exploration of a taut cable and a TMD system

A Tuned Mass Damper-Magnetorheological (TMD-MR) damper that can be placed anywhere along a cable was proposed and tested in the previous study by the writers to overcome the deficiency of the traditional mechanical dampers. In the present study, free vibrations of a taut horizontal cable with an attached TMD model that represents the proposed TMD-MR damper are investigated in detail using analytical formulations of a complex equation of motion, which comes to be an eigenvalue problem in terms of the location of the damper, the mass, and the frequency ratios between the TMD damper and the cable, and the damping ratio of the TMD damper. The solution of this complex eigenvalue problem represents the dynamic characteristics of the cable–damper system. Two special cases (over-damped and zero-damped oscillation) are discussed. Effects of parameters such as the positions and properties of the TMD damper on the system dynamic characteristics are investigated in terms of system modal damping. Parametric results show that a considerable modal damping can be obtained using the TMD damper if an appropriate balance between the TMD component and the MR component is achieved. This numerical procedure provides a basis for a rational design of the TMD-MR damper for any specific cable. A design example is provided for demonstration purposes.