On the effect of the bending stiffness on the damping properties of a tensioned cable with an attached tuned-mass-damper

In this paper the vertical vibrations of a tensioned cable with bending stiffness and with an attached tuned-mass-damper (TMD) will be considered. The damping behavior of a cable with attached damper may be influenced by the bending stiffness of the cable. In this paper the bending stiffness is represented by the non-dimensional parameter a=EI/(TL2)a=EI/(TL2), in which EIEI is the bending stiffness, TT the constant cable tension, and LL the length of the cable. The aim of this paper is to consider the effect of bending stiffness on the dynamics of a cable with an attached TMD. It will be discussed that the TMD is most effective to damp the nnth mode of the undamped cable in the case where the frequency of the damper is tuned to be close to the frequency of this nnth mode. The TMD parameters for which the TMD is most effective are the so-called optimum TMD parameters and result in the corresponding optimum damping rates. These optimum damping rates will be evaluated numerically for a cable without bending stiffness. Then, the influence of the bending stiffness on the damping rates will be studied. In the case where the frequency of the damper is tuned to the frequency of the first mode of the undamped cable, it will be found that a≥10−3a≥10−3 can, depending on the TMD parameters, significantly reduce the damping rates. In the case where the frequency of the damper is tuned to the frequency of the second mode, a≥10−4a≥10−4 can significantly reduce the damping rates.