Semiactive damping of cables with sag

Cables, such as those used in cable-stayed bridges, suspension bridges, guy wires, transmission lines, and flexible space structures, are prone to vibration due to their low inherent damping characteristics. The mitigation of cable vibration is necessary to minimize negative impact. Transversely attached passive viscous dampers have been implemented on some cables to dampen vibration. However, it can be shown that only minimal damping can be added if the damper attachment point is close to the end of the cable. For long cables, passive dampers may provide insufficient supplemental damping to eliminate vibration problems. A recent study by the authors demonstrated that "smart" semiactive damping can provide significantly superior supplemental damping for a cable modeled as a taut string. This article extends the previous work by adding sag, inclination, and axial flexibility to the cable model. The equations of motion are given. A new control-oriented model is developed for cables with sag. Passive, active, and smart (semiactive) dampers are incorporated into the model. Cable response is seen to be reduced by semiactive dampers for a wide range of cable sag and damper location.