# Dynamic Analysis of CRTS II Ballastless Track-Vehicle System Based on Moving Unit Method
## 1 Introduction  
High-speed rail tracks are mainly divided into two types: ballast track and ballastless track. Ballastless track, compared with ballast track, reduces the maintenance workload and cost and increases driving safety and stability of driving; therefore, the ballastless track is becoming increasingly common in high-speed rail [1]. At present, most of the high-speed rail track construction in China, Japan, Germany, and other countries is for ballastless tracks [2]. In recent years, the increase in the speed of high-speed rail has posed new challenges to the safety, comfort, and durability of high-speed rail [3]. Therefore, it is important to establish a reliable ballastless track model for high-speed rail, develop accurate and efficient calculation methods, and study the dynamic performance of high-speed rail ballastless track systems under complex operating environments for the development of ballastless track for high-speed railways in China. Most of the existing studies on ballastless tracks are based on the assumption of the continuous support of track beams, ignoring the additional dynamic response generated by discrete track pads on the track system. To explain the effect of discrete support, [PERSON] et al. [4] investigated the dynamic response of an infinitely long Timoshenko beam supported by discrete sleepers and subject to wheel movement. [PERSON] et al. [5] proposed a cyclic calculation method based on the moving element method (MEM) and used theEuler beam theory to investigate the dynamic response of a high-speed rail system under the discrete support of trackpads. Based on this cyclic calculation method, [PERSON] et al. [6] investigated the excitation of the train-track system by sinusoidal wave discontinuities, substituting a three-layer Timoshenko beam model for the Euler beam model and accounting for the impact of discontinuous supports. Moreover, the issue of discontinuities between neighboring track slabs has been oversimplified in most research. To analyze the dynamic response of a ballastless track system, for instance, [PERSON] et al. [7] suggested a vehicle-track finite element model, where the discontinuity between consecutive track plates was omitted to reduce the thermal expansion effect. According to the study, precast track slabs exhibit stiffness discontinuities at the slab end joints under typical vehicle operation, which poses a serious risk to the track's structural integrity. In the subject of steel-spring floating plate tracks for urban rail transport, where shear hinges are preferred between adjacent floating plates, the issue of discontinuity between track plates has received much attention in previous studies. To examine the restraint impact of shear hinges between track slabs, [PERSON] et al. [8] simulated shear hinges using vertical and transverse shear springs. [PERSON] et al. 's [9] simulation of shear hinges using bending shear spring damping units allowed them to determine the ideal set of parameters for shear hinges between track slabs. In the field of ballastless tracks, there are fewer studies on inter-slab discontinuity; although, some researchers have considered this issue, such as [PERSON] et al. [10] and [PERSON] et al. [11], who modeled the effect of inter-slab discontinuity, but they did not disclose model specifics. In order to address this issue, [PERSON] et al. [12] established an infinitely long beam model for vehicle-track interaction and proposed a cyclic calculation method based on the Euler beam theory for the track plate discontinuity problem, both of which have significant implications for the advancement of ballastless track models. The finite element unit method (FEM) is still the primary technique for analyzing vehicle-track vibration at this time. However, analysis using FEM faces the issue of high computational effort and poor analysis efficiency due to the appreciable rise in the train operating speed [13]. To solve these difficulties in FEM, [PERSON] et al.