ORIGINAL EXPRESSION OF THE TENSION OF A CABLE WITH APPLICATION TO THE OSCILLATIONS OF A MASS SUSPEND

Abstract eng:
Cables are present in many engineering fields such as bridges, elevators, cranes and ropeways. Due to their specific geometry and structure, they exhibit nonlinear properties which have an impact on their dynamic behavior through parametric resonance, leading to noise and vibrations. For example, the performance of a crane may be highly reduced and the transport of people in elevators can be uncomfortable when oscillations are not under control. Consequently, cables have always been of particular interest for industrials and researchers, leading to many different models depending on the applications. A new approach of cables dynamics is presented in this paper. It is based on the exact expression of tension coming from continuum mechanics, while the previous elastic models of cables in open litterature consider an approximation of small strain which reduces the cable to a spring. The equations of a mass suspended to an elastic cable are derived on the basis of this new formulation. The problem is studied and numerically calculated for one and two degrees of freedom. A comparison with the classical approach is presented.

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