FREE TRANSVERSE VIBRATIONS OF A LOAD-BEARING ROPE WITH SPRING-COMPLIANT SUPPORTS AT DIFFERENT LEVELS

Abstract

This article investigates the free transverse vibrations of a load-bearing rope with spring-compliant supports at different levels. The study is motivated by the widespread use of load-bearing ropes in mechanical engineering, transport systems, and construction, where they experience significant dynamic loads that affect structural stability and operational safety. The precise modeling of such systems is essential for understanding their behavior under varying operational conditions and ensuring their long-term reliability.

Using Lagrange’s equation and the geometrical approach to flexible string modeling, a nonlinear differential equation is derived to describe the free transverse vibrations of the rope. A systematic methodology for solving this equation is presented, leading to an analytical expression for the mass reduction coefficient of the system. This coefficient is a crucial parameter for evaluating the dynamic behavior of load-bearing ropes and is determined considering different support levels and a concentrated load acting on the rope. The influence of these factors on the natural frequencies and amplitude of vibrations is thoroughly analyzed.

The study highlights the role of support compliance in altering the dynamic response of the rope. Experimental and theoretical findings indicate that supports with high compliance significantly affect the magnitude of dynamic forces, leading to nonlinear oscillatory behavior and changes in stress distribution along the rope. This aspect is particularly relevant for the design of mobile suspended rope systems, where load stability and oscillatory behavior must be precisely controlled. The results also provide insights into energy dissipation mechanisms and the potential resonance phenomena that may arise in practical applications.

The proposed analytical approach provides an efficient method for predicting the mechanical response of suspended rope structures. The results contribute to the optimization of engineering designs, enabling improved load distribution strategies, enhanced damping techniques, and structural reinforcements to mitigate adverse vibrational effects. The research findings are applicable to crane systems, cableways, suspension bridges, and other mechanical systems relying on load-bearing ropes, ensuring their operational efficiency, safety, and durability under dynamic loading conditions.