Using the Green’s functions method to study wheelset/ballasted track vertical interaction

Abstract

This paper presents an application of the Green’s functions method in the field of the wheelset/track interaction using a new model of the periodic support of the rail that improves the prediction for both low and high frequencies. The track is reduced to a rail modelled as an infinite Timoshenko beam resting on discretely equidistant supports. The model of the periodic support consists of two three-directional Kelvin–Voight systems for the rail pad and the ballast, and a mixed Kelvin–Voigt/Maxwell system for the subgrade. Also, the inertia of the sleeper and the ballast block are introduced. The wheelset is considered as a uniform Timoshenko beam with attached rigid bodies for wheels, axle boxes and brake discs. Only the symmetric bending modes are taken into account and included in the wheel response. The issue of the wheel/rail interaction is solved in the time-domain utilising the Green’s matrix of the track, which includes, in a numeric form, the rail’s response along a span to a moving impulse force, and the time-domain Green’s function of the wheel in order to point out the basic properties of the wheelset/track steady-state interaction. This particular interaction behaviour is dominated by the two parametric resonances due to the first symmetric bending mode and the rigid-body mode of vibration of the wheelset and the corresponding sub-harmonic parametric resonances. The influence of the structural damping of the wheelset axle on the dynamic interaction due to the irregularities of the rolling rail surface is also presented.