ANALYSIS OF TRAIN STOCHASTIC VIBRATING LOADS IN RAILWAY ENVIRONMENTAL VIBRATION

The analytical model for moving vehicle-ballasted (unballasted) track-subgrade-ground vertical coupling vibration and the pseudo-excitation method are effectively combined, and the accurate power spectrums of train stochastic vibrating loads are directly obtained by using the power spectral of track irregularity, then the time histories of train stochastic vibrating loads are solved by the trigonometric series approach in which samplings are conducted in the frequency domain. Thus, a simple and effective method for calculating train stochastic vibrating loads in railway environmental vibration is provided. The power spectrum densities and time histories of train stochastic vibrating loads generated by a CRH3 high speed train for two cases with ballasted track and unballasted track are analyzed in the numerical example. The environmental vibration induced by trains has received a lot of attention from the public and railroad professionals. The analysis of train stochastic vibrating loads is the first step for the railway environmental vibration problems. The train stochastic vibrating load is mainly composed of moving constant load and stochastic vibrating load, in which the constant load is the train axle load and the stochastic vibrating load is the dynamic wheel-rail force caused by track irregularities, and the latter is the major factor 1,2 . Solution of the stochastic vibrating loads requires dynamic analysis of the train-track coupled system influenced by track random irregularities, and the impact of subgrade need to be considered when the railway is located in soft foundation. A lot of achievements 1-6 for calculation of the stochastic vibrating loads have been made by domestic and foreign scholars mainly by using the numerical method 3-6 . Using the conventional numerical methods such as FEM, the various states of train and track can be well simulated and the nonlinear vibration problem of the system can be analyzed. But for the high-speed train, especially when the train-tracksubgrade-ground dynamic coupled system is established in soft foundation, size of the numerical model is large, and calculation time step is short, so theses result in huge computational effort. In addition to numerical method, another method used to solve train stochastic vibrating loads is analytic method. The vibration deformations of foundation and buildings due to running train are small, so the vehicle-track-subgrade-ground coupled system can be considered as a linear system, the analytic method has an obvious advantage for the analysis of the linear system. In the references 1and 2, analytical models of the train-track-ground system were established to analyze the railway environmental vibration, which had considered the train stochastic vibrating loads induced by random track irregularity. In the above analytical model, the track random irregularity is modelled as the