There is always some randomness in the material properties of a structure due to several circumstances and ignoring it increases the threat of inadequate structural safety reserves. A numerical approach is used in this study to consider the spatial variability of structural parameters. Statistical moments of the train and bridge responses were computed using the point estimation method (PEM), and the material characteristics of the bridge were set as random fields following Gaussian random distribution, which were discretized using Karhunen-Loève expansion (KLE). The following steps were carried out and the results are discussed herein. First, using the stochastic finite element method (SFEM), the mean value and standard deviation of dynamic responses of the train-bridge system (TBS) were examined. The effectiveness and accuracy of the computation were then confirmed by comparing the results to the Monte-Carlo simulation (MCS). Next, the influence of the train running speed, bridge vibration frequency, and span of the bridge on dynamic coefficient and dynamic response characteristics of resonance were discussed by using the SFEM. Finally, the lowest limit value of the vibration frequency of the simple supported bridges (SSB) with spans of 24 m, 32 m, and 40 m are presented.

由于多种情况，结构的材料特性总是存在一些随机性，忽视它会增加结构安全储备不足的威胁。本研究使用数值方法来考虑结构参数的空间变异性。使用点估计法（PEM）计算列车和桥梁响应的统计力矩，并将桥梁的材料特性设置为遵循高斯随机分布的随机场，并使用Karhunen-Loève展开（KLE）进行离散化。执行了以下步骤并在本文中讨论了结果。首先，使用随机有限元方法（SFEM）检查车桥系统（TBS）动态响应的平均值和标准偏差。然后通过将结果与蒙特卡罗模拟（MCS）进行比较，证实了计算的有效性和准确性。接下来，利用有限元法讨论了列车运行速度、桥梁振动频率和桥梁跨度对动力系数和共振动力响应特性的影响。最后给出了跨度为24 m、32 m、40 m简支桥(SSB)振动频率的最低限值。