Effective length of beam on elastic foundation under a moving load

Vibrations induced by high-velocity train passing through environmental sensitive area are important issues to railway authorities. Research has been granted to resolve the environmental impact generated from vehicle-track interaction to the neighbor buildings. Models were established to simulate the vehicletrack interaction system which is the source of vibrations. Among them, Euler beam with finite length on elastic foundation subjected to moving loads is most commonly used to simulate the continuous track on site. The reason of modeling infinite length track with finite length model is to make solving possible by numerical analysis. However, the accuracy of analysis depends on the length of the model. If the length of the model is not long enough, the solution may be interfered by reflective waves from the boundary. Effective length, which is the shortest length that makes the result stable, may be determined with many parameters such as velocity, damping ratio, material stiffness, etc. Determination of "effective length" is the key for reliable results. Lacking of universal and efficient approach, trial-and-error was widely adopted to determine the effective length of models in the past research. A neat and efficient guideline was proposed based on the analytical solution of the model of Euler beam on elastic foundation subjected to a moving load with constant velocity. The accuracy and efficiency were discussed to justify the proposed approach.