Stability of traveling, pre-tensioned, heavy cables
We study the dynamics of an inclined tensioned, heavy cable traveling with a constant speed in the vertical plane. The cable is modeled as a beam resisting bending and shear. The governing equation for the transverse in-plane vibrations of the cable are derived through the Newton-Euler method. The cable dynamics is also studied in the limit of zero bending stiffness. In all cases, application of en- ergy balance reveals that the total energy of the system fluctuates even though the oscillations are small and bounded in time, indicating that the system is nonconser- vative. A comprehensive stability analysis is carried out in the parameter space of inclination, traveling speed, pre-tension, bending rigidity and the slenderness of the cable. Effect of damping is also considered. We conclude that, while pre-tension, rigidity and slenderness enhance the stability of the traveling cable, the angle of inclination affects the stability adversely. These results may act as guidelines for safer design and operation.