Response of train-bridge system under intensive seismic excitation by random vibration method

Earthquake is a kind of sudden and destructive random excitation in nature. It is significant to determine the probability distribution characteristics of the corresponding dynamic indicators to ensure the safety and the stability of structures when the intensive seismic excitation, the intensity of which is larger than 7, acts in train-bridge system. Firstly, the motion equations of a two-dimensional train-bridge system under the vertical random excitation of track irregularity and the vertical seismic acceleration are established, where the train subsystem is composed of 8 mutually independent vehicle elements with 48 degrees of freedom, while the single-span simple supported bridge subsystem is composed of 10 2D beam elements with 20 degrees of freedom on beam and 2 large mass degrees of freedom at the support. Secondly, Monte Carlo method and pseudo excitation method are adopted to analyze the statistical parameters of the system. The power spectrum density of random excitation is used to define a series of non-stationary pseudo excitation in pseudo excitation method and the trigonometric series of random vibration history samples in Monte Carlo method, respectively solved by precise integral method and Newmark-beta method through the inter-system iterative procedure. Finally, the results are compared with the case under the weak seismic excitation, and show that the samples of vertical acceleration response of bridge and the offload factor of train obeys the normal distribution. In a high probability, the intensive earthquakes pose a greater threat to the safety and stability of bridges and trains than the weak ones.