THE INTERACTION OF AN INFINITE WHEEL-TRAIN WITH A CONSTANT SPACING BETWEEN THE WHEELS MOVING UNIFORMLY OVER A RAIL TRACK

摘要

A periodic model of rail track in the form of an infinite Timoshenko beam held by massive elastoviscous supports with constant spacing is considered. The sprung part of the carriage is separated from the wheel by an elastic spring, and its action on the wheel in a first approximation is therefore represented by a static load. The steady vertical vibrations of the rail under the action of an infinite train of wheels moving uniformly over the rail are investigated. The distances between the wheels are identical, and all the wheels have the same mass and carry the same load. The static stiffness of the track over a sleeper exceeds that of track in the space between sleepers. Therefore, under the action of a constant load, each wheel performs vertical parametric vibrations with the frequency of passage of the sleepers. These vibrations are an extension of parametric vibrations described using the well-known Mathieu and Hill equations.