Moving force on an axially loaded beam—with applications to a railway overhead contact wire

Abstract

Using modal analysis, the deflection of a beam subjected to an axial tensile force N and a moving vertical force P, has been determined. This solution was exploited in a study of deflection and wave propagation in the contact wire of a railway overhead catenary system. For moderate values of speed c of the moving force P (i.e., c less than half the lowest critical speed c crit) travelling waves reflect at the boundaries of the contact wire so that the waves meet and catch up with the moving force several times. In practice, when a pantograph (here modelled by the force P) touches the contact wire some distance from the end of the wire, waves are sent out both in the forward and backward direction, giving even more reflections and wave interactions with the contact force. These waves will add or subtract to the wire deflection at the point of force application. The stress in the wire due to bending is estimated and it appears to be moderate for the speeds investigated here (i.e., for c<0.5c crit). Close to the critical speed, however, bending stresses will be significant.