Longitudinal resonant oscillations of viscoelastic rope of capacity plants

The resonance properties of the rope hoisting installations are investigated in the article. The object of study refers to a wide range of vibrating one-dimensional objects of variable length. Classical mathematical model used to describe the vibrations. Kantorovich-Galerkin method was used in the solution. The solution has a mode structure, unlike the asymptotic methods, allowing you to analyze the resonance properties of the rope. Neglecting small quantities provides a relatively simple expression for the amplitude of resonance oscillations. The phenomena of resonance and the steady passage through resonance analyzed using the resulting expression. The quantitative characteristics of the resonance properties are given in the article, unlike most of the research in this area. The results are shown in graphs. The decision is made in terms of dimensionless variables, that allows the quantitative results obtained for the analysis of vibrations of technical objects.