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Modeling high-frequency wave propagation in rail tracks for crack detection

This paper gives insight to the ultrasonic wave propagation in arbitrary cross section waveguides such as a rail. Due to the geometrical complexity of the rail cross section, the analytical solution to the wave propagation in the rail is not feasible. A Semi Analytical Finite Element method is described as an alternative yet still robust approach to get the solution of the problem. The free-vibration solution (unforced) and the forced solution to a laser excitation, are shown for the case of an undamped rail up to a frequency of 500 kHz. The effects of different loading patterns are discussed, while experimental results are provided. A mode selection is performed, in accordance to the sensitivity of each mode to the different types of defect that can occur in a rail.