Free Transverse Vibrations of a Load-Bearing Rope with Spring-Compliant Supports at Different Levels

Keywords

load-bearing rope, transverse vibrations, spring-compliant supports, dynamic loads, reduced mass coefficient, rope-load system

Abstract

This paper investigates the free transverse vibrations of a load-bearing rope with spring-compliant supports at different levels. Using Lagrange’s equation and the geometrical approach to flexible string modeling, a nonlinear differential equation was derived to describe the dynamic behavior of the system. Analytical expressions for the reduced mass coefficient were obtained, enabling evaluation of vibration frequencies and amplitudes depending on the rope parameters, load weight, and support compliance. The results demonstrate that spring-compliant supports significantly affect the dynamic response of the system, leading to frequency shifts and increased oscillation amplitudes. The developed methodology can be applied in the design of cableways, suspension bridges, crane systems, and other rope-supported structures.

References

1. Kaplun P., Sliepko T. Free transverse vibrations of a load-bearing rope with spring-compliant supports at different levels // Herald of Khmelnytskyi National University. Technical Sciences. – 2025. – 347. – P. 548–553. https://doi.org/10.31891/2307-5732-2025-347-75