Modal Analysis of a Time-Variable Ropeway System: Model Reduction and Vibration Instability Detection
Abstract
Reliable, safe, and sustainable form of mobility is an important issue in their engineering designs. Ropeways have been used for century for different purposes: their advantages in terms of cost, footprint, and energy efficiency make it as one of the solutions to meet the need for urban mobility. Nevertheless, because of the presence of moving cables and the time-varying modification of the mass repartition and stiffness properties of the system, ropeways are sensitive to the effects of dynamic perturbation and self-sustaining oscillations. So far, the analytical models are generally restricted to a cable span between two supports and are too simple to account for different existing phenomena. From this observation, the present chapter proposes a dynamic analysis based on an original definition of the vibration modes of the ropeway considered in its entirety according to an analytical–numerical approach. The modes are defined for several successive positions of the vehicles along the cable established on a linearized dynamics around a nonlinear static equilibrium state, using an equivalent parametric vision of the modal evolution of the system. Then, a model reduction by projection on a mode identified as problematic for the vibratory behavior is conducted. From the results given by the calculation of the quasi-static evolutions, a Mathieu–Hill type equation with a parametric excitation is obtained. A stability analysis of the reduced model is carried out in order to identify design rules that allow to avoid unstable operating zones likely to generate strong vibrations.