Numerical simulations of large deformation cable dynamics.

Abstract

The objective of this research is to predict the dynamics of a cable subjected to aerodynamic/hydrodynamic forces in both high- and low-tension applications. The cable is modeled as a one-dimensional elastic continuum that is able to support tension, bending and torsion. In essence, the cable is a (non-uniform) elastica that is allowed to undergo arbitrarily large rotations. The resulting equations of motion constitute a nonlinear initial-boundary-value problem. A numerical algorithm is developed based on separate finite differencing in time and in space. The numerical solutions are obtained for two different applications. The first application concerns underwater cables and begins with a cable laid upon an uneven seabed. Contact with local peaks in the seabed can produce low-tension cable suspensions between peaks. These low-tension suspensions are of particular concern, as they may become sites where loops can form. Loops must be avoided in many applications as they can damage or otherwise degrade the performance of the cable. The dynamics of loop formation is studied using simple models of cable suspensions and for a variety of support conditions. Simulations show that loops can form under the action of applied compression and/or torsion and by both in-plane and out-of-plane deformations. The simulations reveal that loops can also be released by in-plane or out-of-plane (pop-out) instabilities. The second application concerns the long and flexible fly line used in the sport of fly casting. This dissertation provides the first application of a cable theory to this application. Two models are developed to simulate the dynamics of a fly line with an attached fly during a standard overhead cast. One model describes only the fly line, with the motion of the tip of the rod being a prescribed boundary condition. The second model couples the fly line to a flexible fly rod with the motion of the caster's hand being a prescribed boundary condition. Numerical results are compared with experimental results and with an analytical approximation based on the work-energy principle.