This paper presents a modified numerical substructure method for simulating the dynamic response of vehicle–track–bridge (VTB) systems. The method can be used to analyze large-scale VTB systems accurately and efficiently. Based on the principle of virtual work, the equations of motion are derived for two separate subsystems, i.e. a small-scale of finely modeled VTB substructure and a coarsely meshed large main bridge subsystem using different level of refinement. Different from the conventional dynamic substructuring approaches, the bridge spans close to the vehicle are modeled in both the main and substructure models, and the contradiction of repeatedly modeling is solved using a “nonlinear force corrector”. A special wheel–rail interaction (WRI) element is used to simulate the fast-moving interaction force between the vehicle and rail. In this way, the two models remain unchanged while the vehicle moves forward, and the computational accuracy is the same as the large-scale purely refined model, while the efficiency is significantly improved, particularly, for the large-scale long VTB systems. Two examples of realistic VTB systems with either smooth or un-smooth rails are used to verify the proposed method. The results demonstrate that the presented method has remarkable advantages of computational efficiency and accuracy, providing a practically useful tool for analysis of large-scale VTB systems.

中文翻译：

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车辆-轨道-桥梁系统动态分析的改进数值子结构方法

本文提出了一种改进的数值子结构方法，用于模拟车辆-轨道-桥梁 (VTB) 系统的动态响应。该方法可用于准确高效地分析大型 VTB 系统。基于虚功原理，推导了两个独立子系统的运动方程，即一个小规模的精细建模的VTB子结构和一个使用不同细化水平的粗网格大型主桥子系统。与传统的动态子结构方法不同，靠近车辆的桥梁跨度在主结构和子结构模型中都进行了建模，并使用“非线性力校正器”解决了重复建模的矛盾。一种特殊的轮轨相互作用 (WRI) 元素用于模拟车辆和轨道之间的快速移动相互作用力。这样，两个模型在车辆前进的过程中保持不变，计算精度与大规模纯细化模型相同，同时效率显着提高，特别是对于大规模长 VTB 系统。两个具有光滑或不光滑轨道的实际 VTB 系统示例用于验证所提出的方法。结果表明，所提出的方法具有计算效率和准确性的显着优势，为大规模VTB系统的分析提供了一种实用的工具。两个具有光滑或不光滑轨道的实际 VTB 系统示例用于验证所提出的方法。结果表明，所提出的方法具有计算效率和准确性的显着优势，为大规模VTB系统的分析提供了一种实用的工具。两个具有光滑或不光滑轨道的实际 VTB 系统示例用于验证所提出的方法。结果表明，所提出的方法具有计算效率和准确性的显着优势，为大规模VTB系统的分析提供了一种实用的工具。