An Analysis of Coupled Extensional-Torsional Oscillations in Wire Rope

Abstract

Coupled extensional-torsional behavior of wire rope is considered. Equations of motion for a straight rope section loaded simultaneously in tension and torque are derived, and constitutive equations relating these loadings to extensional and rotational deformations of the rope are postulated. A pair of wave equations describing coupled extensional-torsional oscillations of a wire rope is then obtained. The solution to these equations shows that, in general, two types of waves can propagate through a straight rope section. Four commonly occurring boundary value problems for a rope stretched between the ocean floor and ocean surface are considered. Each problem has a different combination of end restraints—either clamped or swiveled. A sinusoidal forcing function representing wave action is applied to the upper end of the rope. The critical driving frequencies as a function of rope length are calculated for each boundary value problem. These critical frequencies are compared with those predicted by considering extensional oscillations only. The comparison shows that significant differences exist bewteen the predicted resonant frequencies and demonstrates the importance of examining the torsional behavior of wire rope.