Mechanics of cables with interwire friction

Abstract

This thesis deals with the problem of various mechanical behaviours of cables when interwire dry friction is taken into account. Literature review shows that damping properties of cables due to interwire slippage have been known for a long time. However, most existing theories in cable mechanics neglect the effect of interwire friction and corresponding slippage between the wires and thus are not capable of analyzing the hysteresis in cables. A mathematical mode is developed in which a cable is considered as a system of interacting thin wires with dry friction at the interfaces. Accordingly, a cable behaves as a solid rod before the onset of slip, and as a system of wires, governed by the Love's theory of thin rods, after the slip takes place. Various modes of cable deformations are considered: simple and cyclic extension, uniform and cyclic uniform bending. The origination and propagation of an interwire slip is the special area of interest in this study, since it has not been done before. The slip is a manifestation of internal degrees of freedom in a cable. It is shown that friction losses are caused by the twisting and bending deformations of the wire in an axially loaded cable. The propagation of slippage is found to be a linear function of load. Explicit expressions for the hysteretic losses in a tension cable are derived, which show that they are proportional to the third power of the oscillating load and in inverse proportion to the friction forces. In the case of cyclic deformations, analytical relationships are derived for the loading, unloading and reloading phases of the first cycle. It is shown that the unloading and reloading phases result in a closed hysteretic loop. In the case of bending, a slip is expected to start at the neutral axis of cross section of the cable and it will spread symmetrically toward the outer and inner part of the cable with the increase of bending. Also the critical bending curvature for the onset of slippage, slippage boundary and energy dissipation are derived Bending stiffness of the cable with finite friction is analyzed as well. Numerical examples are given to show the applications of the model. Comparison of the theoretical results with the known experimental data is very encouraging.