基于广义瑞利里兹法与模态综合的车辆-轨道系统建模方法与应用

Modeling method and application of vehicle-track system based ongeneralized Rayleigh-Ritz method and component mode synthesis

轨道作为一种长尺度组合结构,其本身材料性能、下部基础支撑状态具有十分显著的非均匀或随机特性.本文基于车辆-轨道耦合动力学原理,以广义瑞利里兹法和子结构模态综合法为轨道结构的建模思路,构建了一种适用结构截面尺寸、材料刚度等参数非均匀条件下的列车-轨道动力相互作用模型.先以轨道结构为研究对象,选取改进傅里叶级数作为轨道结构的位移基函数,采用能量泛函变分法获取轨道各子结构的模态并进行截断,结合轨道各子结构之间的边界条件对整个轨道系统矩阵进行降阶,将GRRM-CMS用于列车-轨道动力相互作用模型分析.与基于有限单元法的车辆-轨道耦合模型的动力响应结果进行对比,验证了本文模型计算结果的准确性,并量化了轨道结构基函数截断项数、模态选取阶数对动力响应收敛性的影响.最后通过几个算例说明了该模型能够开展各种轨道结构参数非均匀条件下的列车-轨道耦合动力学分析,且具有一定的工程可靠性和适用性.

The railway track, as a long-scale composite structure, exhibits significant non-uniformity or randomness in its material propertiesand the state of its underlying foundation support. In this paper, based on the theory of vehicle-track coupling dynamics, a model forvehicle-track dynamic interaction is constructed using a generalized Rayleigh-Ritz method and component mode synthesis. Thismodel is particularly suited for conditions where the structural cross-section size and material stiffness properties are non-uniform.The study begins with the track structure as the subject of research. An improved Fourier series is chosen as the displacement basisfunction for the track structure. The modal analysis of the track substructures is then conducted using the variational method of energyfunctionals, followed by truncation of these modal forms. The boundary conditions between each substructure of the track areintegrated to reduce the overall system matrix of the track. For the first time, the GRRM-CMS is applied to analyze the vehicle-trackdynamic interaction model. The model’s accuracy is validated by comparing its dynamic response results with those obtained from aFEM-based vehicle-track coupling model. The impact of the number of truncated terms in the track’s basis functions and the selectedmodal order on the convergence of the dynamic response is quantified. Finally, several examples are presented to demonstrate themodel’s capability to perform vehicle-track coupling dynamics analysis under various non-uniform conditions of track structureparameters. The model proves to have considerable engineering reliability and applicability. This approach allows for a more efficientand accurate analysis of complex railway systems, especially in scenarios where traditional methods might fall short due to theinherent non-uniformity and randomness of track properties.