15. Analysis of Medium and High-Frequency Vibration for Track Structure

The ballastless track structure exhibits wide-frequency vibration characteristics under high-speed train loading. While the traditional finite element method is effective for low-frequency structural vibration analysis, it is less suitable for medium- and high-frequency vibration analysis. In this chapter, a frequency-domain vibration model of the vehicle–track system is established based on Spectral Element Method (SEM). The track structure is modeled as a three-layer system using Euler and Timoshenko beams, and the vehicle is represented as a full multi-body model. Based on the exact solutions of the beam wave equation, the dynamic stiffness matrix of spectral elements for the slab track structure is derived. The corresponding spectral element equations are then formulated by applying the boundary conditions. Track irregularities are simulated as virtual excitations via the virtual excitation method. By solving the coupled vehicle–track system equations formulated through the spectral element method, the vibration response of both the vehicle and the track structure in the frequency domain is obtained. The advantages of the spectral element method lie in its modeling flexibility, algorithmic generality, and ease of implementation. It achieves high computational accuracy and efficiency with a small number of elements across a broad range of analysis frequencies.