The Problem of Stability in Mechanical Systems Using the Example of Mine Hoist Installations

Abstract

Investigating the influence of varying shaft steelwork stiffness on the stability of horizontal mass displacements, which are crucial elements of a conveyance-shaft steelwork system, is a significant step in evaluating the risk of parametric vibrations in steel constructions. While the Rayleigh method is limited to the first approximation in the solution to this analysis, it still provides valuable insights. Our examination indicates that the impact of a varying shaft steelwork system may not be noticeable in practical applications. This is a significant finding, as it suggests that the impact of varying stiffness in real working objects may be ignored, because the increase in the parametric resonance effects is negligible. This underscores the importance of our research in understanding the stability of steel constructions. This research, which involves theoretical analysis, simplifies the dynamic analysis of the conveyance-shaft steelwork system’s behavior. The result of the performed analysis is a valuable equation for predicting stable work in real hoist installations.