基于改进点估计法的随机车桥竖向振动分析

Analysis of train-bridge vertical random vibration based on a new point estimate method

铁路混凝土桥梁在施工制造过程中不可避免会造成结构参数的随机性(如混凝土弹性模量、密度等),列车在运营过程由于旅客及货物的随机性会造成列车车体质量的随机性,这些随机性在列车桥梁随机振动中不可忽略。建立了竖向车桥耦合振动模型,利用基于自适应降阶的改进点估计法及Newmark-β积分法编制了随机车桥竖向振动程序,分析了考虑列车车体质量与桥梁结构参数随机的列车、桥梁随机响应的前四阶中心矩,与Monte Carlo法对比结果表明,改进点估计法能够高效精确地计算车桥耦合随机响应,效率提高了2~3个数量级。在得到相应的前四阶中心矩后,通过立方正态变换技术拟合出响应的概率密度函数,该方法可为列车-桥梁极限状态设计提供参考。

In the construction and manufacturing process of railway concrete bridges,the randomness of structural parameters(such as concrete elastic modulus,density,etc.)inevitably exists,the randomness of passengers and cargo may cause the randomness of train-body,mass,and these randomness cannot be ignored in the random dynamics analysis of train-bridge systems.The model of a train-bridge coupled system was established,and the Newmark-βintegral method was used to calculate the first four central moments of random train-bridge dynamic responses based on a new point estimate method which was based on adaptive dimensional decomposition.The results of the comparison with Monte Carlo method show that the new point estimate method can calculate the random response of the train-bridge system efficiently and accurately,and the efficiency is improved by 2—3 orders of magnitude.After obtaining the corresponding first four moments,the probability density function of the response can be fitted by using the cubic normal transformation technique.The method provides a reference to the train bridge limit state design.