Deflection of Pre-Tensioned Flexible Heavy Rope, Fixed in Two Arbitrary Points

Abstract

In this paper, it is obtained the differential equation of sagging of flexible heavy rope stretched at an arbitrary angle to the horizon and its solution in the case of small deflections. It is shown that the maximum deflection is always achieved in the middle of rope projection, and its magnitude does not depend on the position of supports. For the first time in the formulation of the problem, it is assumed that the rope is stretched under the influence of two independent factors: deformation of the prestress and deformation due to gravity, and each of the factors may not be taken into account. It is considered the case of rope deformation in a homogeneous temperature field, and it is established that the presented model becomes incorrect in the case of small pretension in comparison with thermal deformation. For cases of absence of pretension and the equality of temperature deformation and pretension, solutions to the problem are represented for the linearly elastic and rheologically active materials. It is noted methodical features of solving the problem for different stages of creep using the Kelvin-Voigt equation. Solutions are given for the combined use of the Kelvin-Voigt model and linear hereditary viscoelasticity for the primary and secondary creep stages, respectively. The problems of modeling drying and reduction of biological filament are considered.