Abstract: Based on the probability density evolution method (PDEM), the vertical random vibration of the train-track-bridge system was studied. Combined with the idea of orthogonal random function and the reconnaissance theory of number theory, a dimension-reduced method for simulation of representative samples of track irregularity was proposed. The simulation of random excitation representative samples on the level of probability density was realized through two basic random variables. Based on PDEM, the vertical random vibration equation of the train-track-bridge system was established and was verified by a numerical example. The influence of vehicle speed on the random vibration response of the simply supported beam bridge and the CRH3, CRH2 and ICE3 vehicle was discussed. The results show that under the influence of vehicle-bridge resonance, the mean value and standard deviation of the vertical displacement of the midspan of the bridge have the maximum peak value at the speed of 425 km/h; the mean value and standard deviation of the vertical acceleration of the midspan of the bridge basically increase with the increase of vehicle speed; when the main frequency of track irregularity excitation is close to the first vertical natural frequency of the vehicle, the vertical displacement response of the vehicle body is the most significant; the higher the vehicle speed, the greater the contribution of track random irregularity to the vertical acceleration response of the vehicle body.

Key words: railway engineering; train-track-bridge system; random vibration; dimension-reduced simulation; probability density evolution method (PDEM)

摘要： 基于概率密度演化理论（PDEM）开展了车-轨-桥系统竖向随机振动研究。结合正交随机函数思想和数论选点理论，提出了轨道不平顺代表样本的降维模拟方法，通过2个基本随机变量实现了概率密度层次上随机激励代表样本的模拟；基于PDEM建立了车-轨-桥系统竖向随机振动方程，并进行了算例验证；探讨了车速对简支梁桥和CRH3、CRH2和ICE3三种车辆随机振动响应的影响。结果表明：受车桥共振影响，桥梁中跨跨中竖向位移的均值和标准差在车速425 km/h时均出现了最大波峰；桥梁跨中竖向加速度均值和标准差基本呈现随车速的增大而增大变化趋势；当轨道不平顺激励主频接近车辆竖向一阶自振频率时，车体的竖向位移响应最为显著；车速越大，轨道随机不平顺对车体竖向加速度响应的贡献越大。

关键词: 铁道工程；车-轨-桥系统；随机振动；降维模拟；概率密度演化理论