Investigations of Oscillations Rope of Capacity Plants

The article explores the resonance properties of a hoisting rope. The object of the study relates to a wide range of oscillating one-dimensional objects of variable length. A classical mathematical model is used to describe the oscillations. To solve it, the Kantorovich-Galerkin method was used. In contrast to asymptotic methods, the solution has a modal structure, which allows one to analyze the resonance properties of the rope. Neglecting the small quantities made it possible to obtain a relatively simple expression for the amplitude of resonant oscillations. Using the expression obtained, the phenomena of steady-state resonance and transmission through the resonance are analyzed. Unlike most studies in this area, the article provides quantitative characteristics of resonance properties. The solution has been made in dimensionless variables, which allows for the use of the obtained quantitative results for the analysis of fluctuations of technical objects.