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Fatigue damage characterization at the early stage is difficult using conventional inspection methods. Low-frequency nonlinear guided waves have shown promising sensitivity to fatigue damage. However, the frequency pair selection for wave mixing in the quasi-synchronism range relies on numerous trials to achieve good performance of combinational harmonic generation and to reduce the overlapping between the combinational and second harmonics, since an infinite number of combinations can be selected for the frequency pair. In this study, a frequency pair selection method is proposed to simplify these tedious procedures and to provide a guide on the selection of frequency pair for quasi-synchronous wave mixing. The proposed method can be applied to different quasi-synchronous wave modes, and a S-index is introduced to characterize the performance of the combinational harmonic generation. In this study, the fundamental symmetric mode (S0) waves are used for collinear wave mixing. The frequency pairs with different S-indices are used for wave mixing, and to demonstrate the effectiveness and performance of the proposed method on predicting the combinational harmonic generation. The web of a tapered flange beam construction section is modelled in the numerical simulation, which shows similar results as a thick plate and combinational harmonic can be generated. The numerical results show good agreement with the S-index prediction, and the overlapping between combinational and second harmonics decreases with the increase of S-index. The results with lower values of S-index show significant coupling between fundamental harmonics, which results in significant overlapping between combinational and second harmonics. Fatigue damage characterization using quasi-synchronous wave mixing shows the potential to be applied on thick plates. The finding of this study provides a guide on the selection of frequency pair for quasi-synchronous wave mixing.
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