Numerical Study on Propagative Waves in a Periodically Supported Rail Using Periodic Structure Theory

This paper presents the numerical study on propagative waves in a periodically supported rail below 6000 Hz. A periodic rail model, which considers the effects of both the periodic supports and the rail cross section deformation, has been established based on the periodic structure theory and the finite element method. Two selection approaches are proposed to obtain the concerned dispersion curves from the original calculation results of dispersion relations. The differences between the dispersion curves of different support conditions are studied. The propagative waves corresponding to the dispersion curves are identified by the wave modes. The influences of periodic supports on wave modes in pass bands are revealed. Further, the stop band behaviors are investigated in terms of the bounding frequencies, the standing wave characteristics, and the cross-sectional modes. The results show that eight propagative waves with distinct modes exist in a periodically supported rail below 6000 Hz. The differences between the dispersion curves of periodically and continuously supported rails are not obvious, apart from the stop band behaviors. All the bounding-frequency modes of the stop bands are associated with the standing waves. Two bounding-frequency modes of the same stop band can be regarded as two identical standing waves with the longitudinal translation of the quarter-wavelength, one of which is the so-called pinned-pinned resonance.