A Novel Model for Train–Track-Bridge Dynamic Interaction Considering Non-Uniform Structural Parameters and Nonlinear Interlayer Contact

The dynamic characteristics of the track and bridge system change continuously with the mileage and operating environment, exhibiting highly significant nonlinear and nonuniform spatial distribution features. Based on the Generalized Rayleigh–Ritz Method (GRRM) and Component Mode Synthesis (CMS), this work presents a novel method to establish a three-dimensional model of train–track–bridge interaction that considers the nonuniform distribution of track–bridge system parameters and the nonlinear contact between track and bridge layers. Unlike traditional Finite Element Method (FEM) models, the GRRM-based structure employs generalized displacements without nodal degrees of freedom, thus avoiding the complex processes of element discretization and assembly when constructing tracks/bridges with nonuniform physical and geometric parameters. Additionally, when dealing with the nonlinear contact relationship between track and bridge layers, this model does not require incremental or iterative methods. By introducing CMS to truncate the modes of each substructure in the track–bridge system and establishing the reduced-order model of the entire system based on boundary conditions at the coupling interface, the matrix dimensions can be effectively reduced, thereby improving computational efficiency. The accuracy and efficiency of this newly developed train–track–bridge dynamic model have been validated through comparisons with FEM-based models and measured results. Finally, several numerical examples demonstrate the engineering practicality of this model.