# Flow-Induced Vibration Analysis by Simulating a High-Speed Train Pantograph
###### 1 Introduction
Multi-rigid body models [11; 12] consider all pantograph components as rigid bodies and establish the pantograph system's dynamic theoretical model after obtaining the actual dimensions, mass, moment of inertia, and center of mass position of each component. Rigid-flexible hybrid models [13; 14], building on multi-rigid body models, replace components such as the bow head and upper arm with flexible bodies to analyze better the vibration characteristics of deformable parts of the pantograph. Flexible body models typically involve a reasonable simplification of the pantograph structure, then establish models for each pantograph component, and finally create the entire pantograph's flexible body model [15; 16] through appropriate hinge and spring constraints. In summary, the equivalent mass models' assumed equivalent mass, spring stiffness, and damping parameters are considerable and do not account for the flexible deformation of pantograph rods, making them inaccurate and unsuitable for the analysis and design of bow-nets at higher speeds. Multi-rigid body models and rigid-flexible coupling models, which consider all or part of the structure as rigid, overlook the rods' flexible deformation, leading to significant errors under high-speed conditions. Flexible models, with their high accuracy, are suitable for dynamic analysis of high-speed pantographs. Research on the flow-induced vibration of pantographs is broadly categorized into experimental studies and simulation research. Experimental investigations include track tests and wind tunnel experiments. For instance, [PERSON] et al. [17] conducted aerodynamic force testing on the SSS400 type pantograph on the Wuhan-Guangzhou line, examining the impact of aerodynamic forces on pantograph-catenary current collection. [PERSON] et al. [18] carried out tests on high-speed pantographs under crosswind conditions in the FL-9 wind tunnel of the Aviation Industry Aerodynamics Institute, analyzing the aerodynamic forces and wind-induced vibration characteristics of the entire pantograph. [PERSON] et al. [19] undertook real-vehicle tests on the high-speed pantograph on the Beijing-Shanghai pilot section, obtaining measured data on the pantograph's aerodynamic drag, lift, surface pressure,structural stress, and flow-induced vibration. [PERSON] et al. [20] and [PERSON] et al. [21] conducted wind tunnel experiments on the pantograph, validating theoretical analysis results, and found that the theoretical outcomes largely agreed with the wind tunnel experimental results. Incorporating the structural model and aerodynamic characteristics of the pantograph, some researchers have also analyzed the flow-induced vibration of high-speed pantographs. Based on quasi-steady theory, [PERSON] et al. [22] performed aerodynamic simulations on the pantograph, determining the impact of aerodynamic forces on the dynamic contact force of the bow-net. [PERSON] [23] analyzed the fluid-structure interaction characteristics of the pantograph as high-speed trains enter tunnels, examining the deformation and stress characteristics of the pantograph during operation on open tracks. [PERSON] [24] analyzed the aerodynamic characteristics and the strength of the fluid-structure interaction of pantograph components under aerodynamic forces. [PERSON] [25] analyzed the aerodynamic characteristics and stress distribution of high-speed pantographs during open track operation and tunnel passage. [PERSON] [26] investigated the external flow field characteristics of high-speed trains at 400 km/h and the distribution of structural stress and deformation of the pantograph under aerodynamic forces. [PERSON] et al. [27] investigated friction-induced vibration and wire corrugation in metro rigid overhead wire-pantograph systems. A friction coefficient above 0.07 significantly increases self-excited vibration and affects wire corrugation. [PERSON] et al.