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Catenaries are large cable structures which transmit electric current to trains through sliding contact with a pantograph. The finite element method is widely used to model this dynamic interaction problem and obtain the contact force between the pantograph and the catenary. As an alternative, analytical models can also be used to study catenary dynamics, although they require certain simplifications of the features considered in numerical models. In this paper, an analytical model composed of an infinite string and a visco-elastic support is introduced and enhanced by considering a Kelvin-Voigt damping model and the initial height of the contact wire. Considering the finite element (FE) model as a reference, the analytical model parameters are properly adjusted through static and wave propagation analyses to achieve similar behaviour in both the analytical and the FE models. To check the performance of the proposed model, the steady-state response of the pantograph–catenary coupled system is calculated and compared with the results of the FE model. Finally, the analytical model is used to analyse the interference phenomenon produced during two-pantograph operation.

Analytical model of the pantograph–catenary dynamic interaction and comparison with numerical simulations