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Mathematical Problems in Engineering
Volume 2017, Article ID 5872419, 13 pages
Research Article

Study on Transmission Characteristics of Vertical Rail Vibrations in Ballast Track

1MOE Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, Chengdu, China
2School of Civil Engineering, Southwest Jiaotong University, Chengdu, China

Correspondence should be addressed to Ping Wang; nc.ude.utjws@gnipw

Received 27 September 2017; Accepted 22 November 2017; Published 19 December 2017

Academic Editor: Michele Brun

Copyright © 2017 Xi Sheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A plane half-track model and a periodic track-substructure model are established. The spectral element method and spectral transfer matrix method are developed and applied to investigate the track decay rate (TDR) and transmission rate (TR) of the vertical rail vibrations, which can reflect the transmission characteristics in the longitudinal and downward directions, respectively. Furthermore, the effects of different track parameters on TDR and TR are investigated. The results show that the antiresonance frequency of the rail and the out-of-phase resonance frequency of the rail and sleeper form the boundary frequencies of the high-attenuation zone for longwise vibration transmission, where the vibration absorption of the sleeper is significant. The downward transmissibility of vertical rail vibrations is greatest around the antiresonance frequency of the rail. Vertical rail vibrations are primarily transmitted in the downward direction at low frequencies, while they are mainly transmitted along the rail at high frequencies. Stiffer rail pads can make more vibrations transmitted downwards to the sleeper above the antiresonance frequency of the rail, while the changes of other track parameters have different effects on the transmission characteristics. Additionally, a field measurement is performed for verification, and the simulations are well consistent with measurements.