Determination of stresses in hoist ropes for low ascent and descent heights

Abstract

The problem of determining stresses in lifting ropes and the question of longitudinal vibrations of elastic rods, related to it in formulation and methods of solution, have a long history, set out in a recently published monograph by Prof. A. S. Lokshina. As early as 1815, Poisson studied the free vibrations of a prismatic rod with a weight at the end. Without setting out to list all the works that were closest in time, we note Boussinesq’s research on the impact of a body of a certain mass on a conical rod of infinite length, as well as the memoirs of Saint-Venant, who studied the impact of two prismatic and conical rods. The same authors also considered, among other related issues, the question of longitudinal vibrations of a rod with a load at the end. The main results of these authors are presented in the famous book by A. Love.