Cables are fundamental components in numerous technical implementations, such as cable-stayed bridges. As cables are prone to vibration due to e.g. wind, it is necessary to find ways to reduce these oscillations.
This thesis aims to build upon the work conducted by Su et al. [1]; their paper studies the vibration of an inclined cable with an attached Tuned Mass Damper (TMD). In particular, as Su et al. assume that the cable takes the shape of a parabola in equilibrium, the goal is to find a better estimate of the equilibrium configuration of the cable. To this end, this thesis will utilise a modified version of the method used by Caswita [2]; Caswita derives the equations of motion of a cable without any attached mass by applying Lagrangian mechanics.
The results show that the equilibrium position differs meaningfully from a parabola. The ordinary differential equations that Su et al. obtain by using Galerkin’s method are also considerably different when using the alternative equilibrium position. These differences are mainly caused by the fact that the cable hangs on an incline, rather than by the addition of the TMD.