Motion and Stress of an Elastic Cable Due to Impact

Abstract

The motion and stress of an initially straight elastic cable one point of which suddenly moves with a constant vector velocity are studied. Formulas for the phase velocities of waves of constant stress and of waves of constant slope including the effect of initial tension and neglecting lateral contraction are derived. Under these assumptions exact and approximate relations between the impact stress and the distribution of energy in the cable are derived and discussed. The theoretical results (which had been classified for a considerable time) are compared with results from tests on aircraft arresting gears carried out at the Naval Air Engineering Facility (Ship Installations), Philadelphia, Pa.

Jump conditions for strings and sheets from an action principle

“…The bodies are modeled as inextensible curves and surfaces. Physical examples of such discontinuities include peeling fronts of adhesive tapes and coatings [16][17][18][19], lift-off points of chains and ropes moving around pulleys or table edges [2,8,9,20], pick-up points of chains from piles or rigid surfaces [1,6,7,21,22], propagating impacts in cables and membranes [11,[23][24][25][26][27][28][29][30][31][32], geometrically complex propagating kinks in a windblown flag or the tubular body and arms of an Airdancer R [33], brittle cracks, tears, and cuts in sheet materials [17,28,34], and groove structures in impressed bladders. It also seems likely that kinks may form in the transverse waves resulting from hairpin turn maneuvers of towed cables [35][36][37].…”