基于虚拟激励法对高速铁路桥梁垂向共振响应的研究

Research on Vertical Resonance Response of Bridge in Train-bridgeInteractive System Based on Pseudo Excitation Method

轨道不平顺是常见的作用在列车-桥耦合系统的随机激励,其与列车移动轴重效应的确定性激励共同作用,使桥梁共振时的响应具有随机性。为克服单一轨道不平顺空间域样本给计算结果带来的不确定性和多样本计算的低效性,本文采用虚拟激励随机振动分析方法,构建二维车桥耦合系统空间状态方程,考虑轨道不平顺随机激励和确定性轴重激励,在列车以不同速度匀速行驶条件下,借助精细积分法通过全过程迭代过程对该状态方程进行精确高效求解,与传统的蒙特卡罗抽样下的纽马克贝塔法求解结果对比,并确定响应的概率分布模型。分析桥梁发生垂向共振时的时频响应,最终给列车安全过桥提出建议。

Track irregularity is a common random excitation in train-bridge interactive system,which randomizes the bridge resonance response under the joint effect of train moving axle load.Hence,determination of the possibility distribution of bridge resonance response is important to ensure the safety.For the purpose of overcoming the uncertainty and the inefficiency,respectively caused by single-sample track irregularity in spatial domain and by multiple samples calculation,the space state equation of two-dimensional train-bridge interactive system was formulated by using pseudo excitation random vibration analysis method.Considering the random excitation of track irregularity and deterministic axle load excitation,under the condition of the train running at different constant speeds,the precise integral method was adopted to solve the equation efficiently and accurately through the inter-system iteration process.The results were compared with those of the Newmark-βmethod under the Monte Carlo sampling,which helps to determine the possibility distribution model fit for the vertical response of bridge.Finally,the time-frequency response of the bridge was analyzed when the vertical resonance occurred,which helps to guarantee the safety when the train crosses the bridge.