Dynamic response of a two-level catenary to a moving load

An analytical method is proposed for calculating the steady-state response of a two-level catenary to a uniformly moving pantograph. The model for the catenary is composed of two strings (the contact and carrying cables) connected by lumped mass-spring-dashpot elements (hangers), which are positioned equidistantly along the strings. The upper string (carrying cable) is fixed at periodically spaced points. This model is capable of describing a coupled wave dynamics of both the carrying cable and the contact cable of the catenary. The pantograph is modelled by a point load, which moves uniformly along the contact cable. Using the proposed method, the steady-state deflection of the contact cable is analyzed thoroughly. Additionally, the contact force between the hangers and the contact cable is studied, which is important for estimation of the fatigue life of the hangers. Two simplified models of the two-level catenary are introduced and studied. The first model assumes that the carrying cable is infinitely stiff, whereas the second model disregards the discrete character of the hangers. Predictions of these simplified models are compared to those of the original model.