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Rails have many ultrasonic guided wave modes, which makes it difficult to determine the suitable guided wave mode and its excitation method. In this paper, the dispersion characteristics of guided waves propagated in rails are studied using the semi-analytical finite element method (SAFEM). High-precision imaging of rail defects is achieved using the symbolic coherent factor total focusing method (SCF-TFM). First, the SAFEM discretized the 3D rail into 2D cross sections to simplify the solving process of the propagation characteristics of guided waves. We introduced rail characteristic parameters into the wave equation and used a transformation matrix T to establish the relationship between wavenumber and frequency, and obtained the dispersion characteristics and vibrational characteristics of the guided wave from 0 to 500 kHz. Second, the RGB images and binary images of the selected mode were analyzed to determine the position and excitation direction of the selected mode. Finally, SCF-TFM was applied to characterize the defects. The sidelobe amplitude and main lobe width of acoustic beams were suppressed, and the ultrasonic imaging precision was improved. Experimental results showed that the proposed method had high detection accuracy with a defect localization error of 0.1% and a size error of 11.5%.
Zhu et al. (Mon,) studied this question.