Nonlinear Impulsive Motions of Low‐Tension Cables

Abstract

Perfectly flexible cables with zero or low initial tension, subject to impulsive loads, have different dynamics than taut cables. The initial transient motion is that of an inextensible cable, and the resulting equations of impulsive, three‐dimensional response show that the developing velocities and tensions depend only on the curvature and not on the geometric torsion of the configuration of the cable. Furthermore, singularities may develop when either the curvature becomes zero, or its derivative is discontinuous. This singularity is removed by introducing the small bending stiffness of the cable. Boundary layers develop, however, having length proportional to the square root of the bending stiffness. Numerical simulations establish the validity of the methodology, and are applied, in conjunction with perturbation methods, to study the response of a freely hanging chain that provides a canonical example of transition from high‐ to low‐tension behavior.