Study on the Dynamic Response of Track Structure under Moving Loads with Variable Speeds

A periodic form solution of the track structure under moving train loads with variable speeds is introduced. The track is simplified as Timoshenko beam periodically supported with spring-damper elements. Firstly, the general dynamical response induced by moving loads on an elastic semi-infinite space is obtained on the basis of Duhamel Integral and Dynamic Reciprocity Theorem. Secondly, in the case of periodic track structure, the general dynamical response equation in the frequency domain is simplified in a form of summation within the track sleeper period instead of integral, which is obtained by transferring the moving loads on the rail to the moving of vibration pick-up point backward within periodic sleeper distance. In this way, the track response induced by the moving loads can be obtained by the calculation program. The train load is respectively modeled as constant moving force, single degree of freedom moving mass and two degree of freedom moving mass system. The calculation results indicate that: with the same passing speed of the loads, the induced vibration under the accelerated load is bigger than that under the constant-speed load; The frequency characteristic of the induced vibration is closely related to the time of the loads passing the sleeper spacing with the pick-up point and reflecting the self-frequency of the moving mass system; The interactive force between the moving mass and the track is much bigger than the gravity of the mass, and it is inaccurate to model the vehicle to be constant moving force.