Wheel–Rail Vertical Vibration Due to Random Roughness in the Presence of the Rail Dampers with Mixed Damping System

In this paper, the vibration of a wheel running on a light rail equipped with rail dampers that use a mixed damping system (rubber–oil) is investigated under the excitation of random roughness on the rolling surfaces, to demonstrate the influence of such rail dampers on the dynamic behaviour at the wheel–rail interface. For this purpose, a model is adopted in which a rigid wheel moves at constant speed over a rail modelled as an infinite Timoshenko beam, supported by elastic foundations with an internal degree of freedom that represents the behaviour of the rail pads, sleepers, and ballast. The rail dampers are represented as two-mass oscillators, while the internal friction in the elastic components of the wheel–rail system is modelled using hysteretic damping. To obtain the time series of the rail and wheel displacements, as well as the wheel–rail contact force, the convolution theorem is applied in a heuristic manner, making use of the relationship between Green’s functions in the time and frequency domains through direct and inverse Fourier transforms. The results show that (a) rail dampers primarily affect rail dynamics and the wheel–rail contact force over a relatively wide frequency range, while having little influence on wheel motion; (b) rail dampers are highly effective in reducing rail vibration and the wheel–rail contact force when the rail pads are stiff, but considerably less effective when soft rail pads are used; and (c) they may slightly amplify the contact force at the lower edge of their effective frequency range.