Identification of Vibration Modes and Wave Propagation of Operational Rails by Multipoint Hammering and Reciprocity Theorem

Vertical bending vibration modes and rail wave propagation, including the damping characteristics, are the factors that cause rail corrugation. However, the ability to identify actual railways has been limited because of the huge number of sensors required for field tests. In this study, a novel and field-applicable method for identifying rail vibration modes and wave propagation characteristics is developed by multipoint hammering and the reciprocity theorem instead of multipoint measuring. Additionally, the proposed method is applied to an actual rail with a direct fastening track system on a bridge that has corrugation with a wavelength of approximately 0.04 m. As a result, the wavelength (wavenumber)-, group velocity-, and distance damping (attenuation) frequency relationship of the wave propagation is clarified in addition to the rail frequencies and mode shapes up to approximately 1500 Hz, including the pinned-pinned mode. Finally, the identified wavelength-frequency relationships and the measured rail irregularity can empirically demonstrate that the generated corrugation on the rail is produced by wave interference on the two axles in the bogie.