Large Deformations of a Whirling Elastic Cable

Abstract

The large deformations of a whirling elastic cable is studied. The ends of the cable are hinged but otherwise free to translate along the rotational axis. The nonlinear governing equations depend on a rotation-elasticity parameter J. Bifurcation about the straight, axially rotating case occurs when J is greater than or equal to n(pi). Perturbation solutions about the bifurcation points and matched asymptotic solutions for large J are found to second order. Exact numerical solutions are obtained using quasi-Newton and homotopy methods.