Mathematical Simulation of Cross-Wind Vibrations in a Mono-Cable Chair Ropeway

摘要

In recent years, chair ropeways used in skiing grounds or sightseeing places in Bulgaria have been adopted as basic means of transport, by virtue of their adaptability and low construction cost as compared to normal roads. However, the largest disadvantage of those cable structures is their weakness to wind influence. Because of their slender structure, transporters suspended by cables are easily affected by the drags of wind. The paper discusses the dynamic behaviour of the chairs and the rope in a span of a mono-cable chair ropeway. A 3D mechanical model of a multibody elastic system has been created. The chairs are presented as pendulums hanging on deformable elements whose elasticity depends on the position of pendulums inside the span and varies in time. The rope has been modelled as massless cable. Only the lateral vibrations of the rope, due to longitudinal motion of the chairs and gusts of the cross-wind loading have been studied. The wind is introduced as a uniform distributed load varying randomly in place and time. The dynamics of each chair has been described by differential equations whereas that of the rope has been expressed by partial differential equations. The slenderness of the supporting structure has been specially examined. All functions of the vertical and lateral vibrations and swinging of the chairs as well as the lateral macro-vibrations of the rope are numerical ones. The derived analytical equations are solved simultaneously by MatLab software. The results have been presented graphically and the simulation of the dynamic process has been animated. The created program is user-friendly and easily adaptable.