Dynamics of the catenary modelled by a periodical structure

In the paper, a dynamic analysis of a two-level model of the catenary which takes into account periodic distribution of hangers and supports is provided. An analytical method is proposed for calculating the response of the catenary to a uniformly moving pantograph. The model of the catenary is composed of two strings (the contact and carrying cables) connected by lumped mass-spring-dashpot elements equidistantly positioned along the strings. These elements are assumed to be visco-elastic. The pantograph is modelled by a concentrated force which moves along the contact cable. The force exerted by the pantograph varies harmonically. This model is capable of describing coupled wave dynamics of the catenary. The proposed method of calculations is based on the Fourier transformation and, therefore, is applicable only to linear models of the catenary. In the analysis, the periodicity condition is used. The spectral analysis is carried out. General results are illustrated by a numerical example in which the effect of wave propagation is visible.