Displacement Field Due To A Moving Load On Euler Beam Resting On An Elastic Half-Space

Track system consists of track, sleeper and gravel cushion. Wheels interact with the track while train is running. During this progress, bending deformation of the track generates and moves along the direction of movement of the train. Due to this bending deformation, elastic wave in the soil near the track generates and propagates outwards. Displacements of the surface of elastic half-space under moving load was analyzed and calculated in this paper in order to evaluate the effect of the vibration of track system on environment along the track line.Based on the mechanism of the generation and propagation of vibration, the track system was simplified to be an Euler beam on the elastic half-space and the train was considered as a moving load on Euler beam. The definition of equivalent stiffness of elastic half-space was used herein to obtain the solution of contact reaction between the beam and the surface of half-space. After analysis, contact reaction of the surface of foundation was found to be a moving load that has fixed distribution, and its velocity is equal to the velocity of the moving load.In order to calculate displacement field of half-space under the moving load on the Euler beam, the contact reaction of the surface of foundation was treated as a series of pulse on the surface of half-space. Displacements of the surface of elastic half-space were obtained from the superimposition of elastic waves caused by those pulses with time delays according to the characteristic of the contact reaction of the surface of foundation. The elastic wave of each pulse was calculated by analytic formula for vibration of the surface of elastic foundation under arbitrary excitations. The time delay of each pulse was determined by its exciting time and the distance between its exciting position and the receiving point. Based on works mentioned above, a new mechanism for generating moving load was synthesized.Vertical displacements of six points in a rectangular array were calculated and characteristics of time histories of these points were analyzed. Afterwards, relationships between the amplitude, time delay and location of each point were compared and autocorrelation function, cross correlation function, auto power spectrum and cross power spectrum of these two points were calculated and analyzed.