# Flow-Induced Vibration Analysis by Simulating a High-Speed Train Pantograph
###### 1 Introduction  
With the increase in the operational speeds of trains, the aerodynamic loads experienced by the trains increase proportionally with the square of the speed. The complex environments in which high-speed trains operate lead to significant increases in the vertical, longitudinal, and lateral vibrations of the pantographs under aerodynamic load. This results in an exacerbation of pantograph disengagement and a severe deterioration in current collection quality. Additionally, the dynamic loads make the pantograph components susceptible to fatigue damage, thus making the analysis of flow-induced vibrations a critical consideration in the design of high-speed pantographs. Currently, research on the pantograph-airflow interaction, both domestically and internationally, primarily focuses on three aspects: the aerodynamics of pantographs, structural vibrations, and flow-induced vibrations. The study of the aerodynamic characteristics of pantographs is mainly conducted through experimental research and numerical calculations. A significant number of scholars have used experimental methods to study the aerodynamic properties of pantographs. For instance, [PERSON] et al. [1] conducted wind tunnel experiments on the aerodynamic characteristics of Faiveley CX type pantographs under crosswind conditions using sensor technology to measure the aerodynamic force coefficients of pantograph components andarticulations. [PERSON] et al. [2] tested the aerodynamic drag and lift on Faiveley pantographs at speeds of 400 km/h to 600 km/h under raised and lowered conditions in a 2.4 m \(\times\) 2.4 m wind tunnel. Additionally, numerical calculation methods typically involve creating aerodynamic models of pantographs and using fluid analysis software combined with turbulence models such as RANS to analyze the aerodynamic performance of pantographs. For example, [PERSON] et al. [3] utilized Fluent to establish a steady-state aerodynamic fluid calculation model of pantographs, analyzing the impact of aerodynamic forces on the contact pressure between the pantograph and overhead wires. [PERSON] et al. [4] calculated the unsteady aerodynamic forces on various components of pantographs using Fluent software 6. [PERSON] et al. [5] developed a fluid simulation model of pantographs, analyzing the surface pressure and lift force. Based on the N-S equations and k-\(\epsilon\) turbulence models, [PERSON] et al. [6; 7] constructed a model for calculating the aerodynamic lift force on pantographs and analyzed the lift force as high-speed trains pass through tunnels at 350 km/h. [PERSON] [8] analyzed the variation in aerodynamic characteristics of pantograph components under crosswind conditions and optimized the aerodynamic shape of some pantograph structures. [PERSON] et al. [9] analyzed the impact of pantograph structural displacement on aerodynamic lift force. Given the pantograph's complex three-dimensional shape, the high-speed airflow causes numerous vortices to shed, resulting in unsteady vibrations under the aerodynamic load. Since steady methods only provide average flow field information, they cannot adequately capture the fluctuations and spectral characteristics of aerodynamic forces. Therefore, to study the flow-induced vibrations of high-speed train pantographs, it is essential to investigate the unsteady aerodynamic performance of pantographs. In terms of structural vibration analysis of pantographs, the models used include the following: equivalent mass models, multi-rigid body models, rigid-flexible hybrid models, and flexible body models. The equivalent mass model simulates the pantograph with mass blocks, springs, and dampers, generally categorized into single-mass block models, two-mass block models, and multi-mass block models. By establishing a two-mass lock model of the pantograph, [PERSON] et al. [10] studied its static and dynamic characteristics, verified through experiments.