Keywords: bicable ropeway, multi-span cable, moving cable cars, nonlinear vibrations, time-domain simulation.

In the first part of this paper the authors present a modified formulation of the multi-span bicable ropeway model proposed in [1,2], which is updated to comply with the assumption of a steep slope of a cableway track. In-plane vibrations of the carrying cable subjected to in-service load due to a set of moving passenger carriers are considered. It is assumed that the carriers modelled by physical pendulums move with constant operational speed along the cable track, the inclination of which is defined by an average slope angle. First, nonlinear partial differential equations describing the vibrations of an inclined multi-span cable are presented in a time-and-space domain. Then, energy formulas are derived and equations for the cable motion are formulated in a time-domain using Lagrangian principles and a Ritz approximation of cable displacements. These equations, completed with a set of equations governing the carriers motion, are finally presented in a compact matrix form which reveals that the motion of two sub-systems: carrying cable and cars, is always coupled, both in the linear and nonlinear problem, when the cable track is inclined. Couplings result from the interaction between cable and carriers and they are expressed by linear components dependent on the cable track inclination and nonlinear ones having an origin in the second order effects.

The above theoretical analysis has been validated in the second part of this study, using numerical application. To solve the problem of nonlinearity, a newly developed computing method is proposed, where angular displacements of pendulums are initially predicated by using parabolic extrapolation and a Newmark scheme is applied to the numerical integration of the equations of motion. The starting conditions are defined by taking into account the short-duration impulsive load appearing when the carrier leaves at slow-speed from a station area and is reattached to the hauling rope. The vibration analysis has been performed for a particular bicable ropeway system subjected to an in-service moving load in a form of one cable car or a semi-infinite flow of carriers. The results of numerical investigations proved that the nonlinear components of cable-car interaction are not significant and can be neglected in vibration analysis. This conclusion will be useful in future research where wind-induced vibrations of operating cableways are going to be considered.

1

M. Knawa, D. Bryja, "Vibrations of carrying cable of ropeway system loaded by passenger carriers modelled by series of moving pendulums", Proceedings of 7th European Conference on Structural Dynamics, Southampton, Great Britain, CD, E115, 2008.

2

M. Knawa, D. Bryja, "Effects of dynamic loads acting on a carrying cable in operating ropeway system", Proceedings of Applied Mathematics and Mechanics PAMM, 8, 10297-10298, 2008.

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