Analytical Investigation of Performance of Passive Negative Stiffness Damper in Two-Cable Hybrid Network

Stay cables in cable-stayed bridges are susceptible to vibrations due to their inherent flexibility and low damping. Different countermeasures to control such vibrations have been extensively researched as well as implemented on actual bridges. New techniques for mitigating stay cable vibrations are still needed as longer cable-stayed bridges are being planned and built. External passive/active dampers and crosstied cable networks are the most effective solutions in controlling undesired cable vibrations. Design aids for the selection of passive damper parameters are available for zero, positive, and negative stiffness dampers (ZSDs, PSDs, and NSDs) installed on a single cable. However, the potential of using passive NSDs in a hybrid cable network, which is a combination of crossties and external dampers, has not been explored. This study presents an analytical investigation on the performance of a passive NSD for vibration control in a two-cable hybrid network. It is revealed that in the case of a hybrid network with NSDs, the stability limit of the system is increased as compared with a single negatively damped cable in addition to a significant improvement in system damping without compromising its in-plane stiffness. The influence of major system parameters on the system stability limit and the damping ratio is discussed. The concept of damping contour for a typical hybrid network is adopted to illustrate selection of the required level of damping for a particular combination of damper location and negative stiffness. The effect of negative stiffness on higher modes is investigated and found to be beneficial for the majority of the modes.