Three-dimensional flexural and torsional mechanics of low and high tension cables

A theoretical model governing the two-axis flexure, torsion and extension of an elastic cable is derived and employed in two major studies. The first study focuses on the nonlinear mechanics of low tension cables which are dominated by cable flexure and torsion. For this low tension regime, this study contributes a nonlinear model and unified analysis for evaluating the existence and stability of globally large cable equilibrium states. The second study considers the dynamic response of high tension cables and the influence of cable flexure local to the suspension end points. For this high tension regime, the dynamic response is largely governed by extension. An asymptotic model tailored to this regime is derived which also captures the effects of cable flexure. This model is well suited for further studies of cable abrasion.; The study of low tension mechanics examines the nonlinear boundary value problem governing globally nonlinear, three-dimensional (spatial) equilibrium states. For the class of problems for which steady loads are applied through the boundaries, this boundary value problem is integrable and admits closed-form elliptic integral solutions. Capitalizing on this observation, closed-form solutions are derived for the complex spatial equilibria obtained numerically by Rosenthal (1975 and 1976) for a cable subject to uni-axial torque and thrust. A companion stability analysis, leads to new and important stability conclusions and demonstrates that many of the planar and spatial equilibria presented by Rosenthal are unstable (unrealizable). The existence and stability criteria are controlled by two principal parameters. These findings are extended to the class of non-integrable problems via numerical analysis. A non-integrable problem is evaluated which describes a u-joint supported cable subject to self-weight and to uni-axial torque and thrust. The self-weight introduces symmetry breaking effects and the u-joint supports introduce support reactions. Despite these added complications, the existence and stability criterion remain simple and, in this case, are controlled by three principal parameters.; The goal of the second study is to model and evaluate the effects of cable flexure in taut suspensions near cable terminations where abrasion mechanisms exist. To this end, an extended model of taut cable dynamics is derived which describes local (linear) three-dimensional dynamic response about a slightly curved planar cable equilibrium. This model is governed by three principal effects: (1) the static tension, (2) the dynamic tension, and (3) the bending stiffness. The bending stiffness represents a singular perturbation of a cable-beam model. This fact necessitates the use of singular perturbation methods for evaluating the dynamic response of nearly-flexible cables. Analysis of this model leads to a fundamental understanding of vibration characteristics and dynamic reactions.