Stability of Vertically Traveling, Pre-tensioned, Heavy Cables

Abstract

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 energy 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 nonconservative. 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.