| Many cable-stayed bridges around the world have exhibited excessive wind-induced vibrations of the main stays, inducing undue stresses and fatigue in the cables. To suppress these vibrations, fluid dampers are often attached to stays near the anchorages. To enable effective and economical design of such dampers, it is important to develop a thorough understanding of the dynamics of a stay cable with attached damper.; To investigate the dynamics of the cable-damper system, a fairly simple model is first considered: a taut string with linear viscous damper. An analytical formulation of the free vibration problem is used to explore the solution characteristics, revealing that damper-induced frequency shifts play an important role in characterizing the response of the system due to the concentrated nature of the damping force. A critical value of the damper coefficient is identified, and for a supercritical damper, certain modes of vibration are completely suppressed, while others emerge, including a non-oscillatory decaying mode.; The influence of bending stiffness is considered using a dynamic stiffness formulation of the free-vibration problem for a tensioned beam with attached damper. Many of the solution characteristics observed in this case are reminiscent of those for the taut string, and damper-induced frequency shifts are again important. The nature of the boundary conditions has a significant effect when bending stiffness is appreciable, and for a damper located near the end of a tensioned beam, significantly higher damping ratios can be achieved if the supports are not fixed against rotation.; Dampers can also have nonlinear characteristics, either unintentionally or by design, and equivalent linear solutions are developed for the vibrations of a taut string with two different types of nonlinear dampers: a power-law damper and a viscous damper with a friction threshold. Relevant nondimensional parameter groupings are identified, and asymptotic approximations are obtained relating these nondimensional parameters to the modal damping ratios for cases when the damper-induced frequency shifts are small. The nature of the dependence of nonlinear damper performance on the amplitude and mode of vibration is investigated, revealing some potential advantages that may be offered by a nonlinear damper over a linear damper. |
