Characteristics of defect states in periodic railway track structure

To overcome the ill-conditioned matrix problem of the traditional transfer matrix method, the Floquet transform method and supercell technology are used to study the defect states of the periodic track structure. By solving the equations of the supercell directly, the propagation characteristics of elastic waves in the track structure with defects are analyzed. The existence of defects destroys the periodicity of track structure, thus resulting in the formation of defect states within the band gaps. Moreover, the elastic wave is localized near the defect position at the frequency of the defect state. The formation mechanism of the defect state in track structure can be explained by the local resonance at the defect. With the expansion of the defect range, the number of local resonance modes that can be formed near the defect increases, thus generating multiple defect states. Furthermore, the defect state enhances the vibration of the structure adjacent to the defect. Therefore, the vibration transmission coefficient in a finite-length range can be used to detect the defect characteristics in the track structure, and the defect degree can be evaluated by the peak frequency of the vibration transmission coefficient within the band gap.