# Vibration Response Analysis of Overhead System Regarding Train-Track-Bridge Dynamic Interaction
###### Abstract  
Based on the paucity of studies on the analysis of the coupled vibration response of the train-track-overhead System, in this article, finite element software ABAQUS was integrated with multi-body dynamics software, Universal Mechanism (UM), to construct a joint simulation model of the train-track overhead system under a railway line, with the focus on the investigation of the influence of different track irregularity levels, speeds and damping coefficients on the coupled vibration response of the vehicle-track-overhead system. The findings demonstrate that the response of the train body is sensitive to track irregularity, which primarily impacts the safety index of train operation. The results also suggest that the level of track irregularity should be rigorously regulated above AAR5 during construction. The train-track-overhead system functions well and satisfies the overhead system's design requirements when the train travels through the reinforced line at a speed of no more than 60 km/h. When the train speed is 100 km/h, the vertical acceleration exceeds the limit for the \"I\" overhead system. There is a possibility of excessive lateral acceleration of the train body and excessive lateral force of the wheel and rail when the train speed is greater than 60 km/h, which endangers the safety of the driver. While it has little effect on the mid-span and vertical displacements, the damping factor of the bridge has a substantial impact on the vertical acceleration and mid-span acceleration of the vertical and  
tools. [PERSON] et al. [3] proposed a linear complementary method to describe the wheel-rail separation in train bridge dynamic interaction, which can avoid the traditional trial and error iterative process in two-dimensional space. [PERSON] and [PERSON] [4] created a robust algorithm for analyzing train track structure interaction, in which the train and substructure are modeled separately and then coupled by contact force via the Lagrange multiplier. Subsequently, [PERSON] et al. [5] proposed a train bridge interaction dynamic analysis scheme based on a local Lagrange multiplier that allowed for the partitioning and non-iterative dynamic analysis of train and bridge subsystems. [PERSON] et al. [6] proposed a new structural characteristic formula of train bridge interaction elements that can more realistically capture the response of the bridge and train. Except for the advancement in coupling train-bridge interactions, recently, the focus of research has shifted to the vibration of structures subjected to train bridge coupling. [PERSON] [7], based on the background of the Yujiang bridge in the Nanguang line, established a refined numerical simulation model for coupled vibration analysis of a train-bridge system. The space vibration responses are calculated by co-simulation based on multi-body system dynamics and the finite element method when the ICE EMU train passes the long-span cable-stayed bridge at different speeds. [PERSON] [8] established a complete vertical analysis model of the train track bridge coupling system and the vibration differential equations of the coupling system. The influence of track irregularity level, train running speed, and train suspension parameters on the dynamic response of the train track bridge coupling system are analyzed and compared, and the sensitive irregularity wavelength range of trains at different speeds is obtained. The results show that the higher the train speed, the greater the ride comfort index, and the longer the irregularity wavelength, the larger the influence range. [PERSON] [9] transformed the track irregularity excitation into virtual excitation using the virtual excitation method of random vibration, and by using MATLAB software, he was able to resolve the virtual response problem with the system by employing numerical separation and iteration. Later, the time-varying power spectrum and standard deviation of the train and bridge subsystem's random response were obtained, and the system's random vibration properties were examined.