Mode selection of nonlinear Lamb wave based on approximate phase velocity matching

In the ultrasonic detection using nonlinear Lamb wave, only the cumulative second-harmonic Lamb wave is useful for the nondestructive evaluation of plate-like structures. One of the conditions for cumulative second harmonic Lamb wave generation is phase velocity matching between the primary and the secondary wave. However, in most cases, the phase velocities are approximate matching. In this paper, we theoretically analyzed and discussed the cumulative effect of second-harmonic Lamb wave. The theoretical results show that, when the phase velocities of the primary and the secondary Lamb waves are approximate matching, there is still a cumulative effect in the secondary wave within a specific distance, which is referred as accumulation distance. Based on the accumulation distance, an excitation window is proposed as the basis for mode selection and excitation condition determination of nonlinear Lamb wave. It is considered that, in the case of approximate phase velocity matching, the mode pair with larger excitation window could generate second-harmonic Lamb wave easier than the other mode pairs. Then, the excitation windows of different Lamb wave mode pairs are calculated and compared theoretically. In order to verify the validity of the excitation window as the basis for mode selection, the ranges of two mode pairs' primary Lamb wave that could generate cumulative second harmonic Lamb wave are measured and compared in a specific plate. In the experiment, the primary and the secondary Lamb waves around a longitudinal mode pair and a crossing mode pair are excited and measured using wedge piezoelectric transducers. In the measurement, the second-harmonic Lamb wave is generated by the primary wave in different frequency and phase velocity ranges, and then the ranges of the primary Lamb wave are confirmed in the phase velocity dispersion curves, using the time-frequency analysis. The experimental result shows that, the primary wave range of the longitudinal mode pair is larger than that of the crossing mode pair, which means that the selected longitudinal mode pair could generate second-harmonic Lamb wave easier than another one. The experimental result is in accordance with the comparing result of the excitation windows. The theoretical and experimental results show that, the excitation window could be an indicator for mode selection and excitation condition determination of cumulative second-harmonic Lamb wave generation, and it can be used in the field of ultrasonic detection using nonlinear Lamb wave.