Damping of Taut-Cable Systems: Effects of Linear Elastic Spring Support

Abstract

The influence of linear elastic support on the damper effectiveness of a cable-damper system was investigated by modeling the system as a taut string, an intermediate damper, and a spring in series. Two types of damper were analyzed in this study: (1) the linear elastic damper; and (2) the friction threshold. An exact formulation for the free vibration of the system was developed for the linear viscous damping system, and a complex eigenfrequencies equation was worked to obtain the explicit solution for the frequency shift. A damping ratio equation for different modes, which depicts the effect of the spring, was developed from the frequency shift. An effective flexibility coefficient was introduced to investigate the effect of different values of support stiffness on the effectiveness of the linear viscous damper. A universal curve family diagram was constructed, which indicated that linear elastic support reduces the effectiveness of the linear viscous damper. The universal curve obtained previously by Main and Jones was a special case of this universal curve family for the case in which the stiffness of the support approached infinity. The equation of maximum force introduced to the spring was also derived and was shown to be positively related to the cable tension force and the cable vibration amplitude at the damper attachment location. The influence of the linear elastic support on a cable-damper system with a friction threshold was also investigated by using the result of the linear viscous damper and the equivalent energy method. The result showed that the linear elastic support also reduces the effectiveness of the friction threshold. An equation showing how to select an optimal friction threshold for a stay cable was also proposed.