Numerical and experimental investigations on second-order combined harmonic generation of Lamb wave mixing

The generation of second- and third-order combined harmonics induced by the interaction of two primary Lamb waves with different frequencies has been analyzed theoretically and observed experimentally in our previous research [W. Li et al., J. Appl. Phys. 124, 044901 (2018)]. However, only third-order combined harmonics were observed experimentally because in the experimental investigations, the conditions for both synchronism and the symmetric feature were not satisfied simultaneously for the generation of the second-order combined harmonics. In this paper, first, the numerical perspective of the second-order combined harmonic generation by the collinear interaction of two primary Lamb waves with different frequencies in an isotropic and homogeneous plate is investigated. The results indicate that the synchronism and symmetric feature of two primary Lamb waves selected significantly affect the generation of second-order combined harmonics at the mixing frequencies. Next, an experimental scheme is proposed to measure the second-order combined harmonics predicted theoretically and numerically, through which it is found that the experimental results agree well with that of the theoretical and numerical predictions. The numerical and experimental results in this paper provide a clear physical insight, not previously available, into the second-order combined harmonic generation induced by the collinear interaction of two primary ultrasonic Lamb waves.