Abstract
A mathematical model that predicts the vibration of wheel/rail systems excited by multiple wheels has been developed. A track is modeled as an Euler beam of infinite length, periodically supported by a system comprised of two springs and a mass. In this system the components represent the following: the two springs, rail pad and ballast stiffness; the mass, a sleeper. A wheel is represented by a single mass. Two sources of vibration are taken into account in the model: the varying stiffness of track between the sleepers and an irregularity on the railhead. On the assumption that any response would be repeated at sleeper intervals, a solution is derived by first equating the value of Fourier coefficients of the wheel locus and that of the rail displacement. The method is applied to the analysis of the vibration of a rail excited by two bogie wheels passing in succession. A sinusoidal irregularity with the wavelength of the sleeper spacing or higher is supposed to exist on the railhead. The results show the basic characteristics of rail vibration such as Doppler shift due to wheel movement, response variations with the irregularity wavelengths and vibration amplitude distribution that is strongly affected by the interference of the two wheels.
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