Generation mechanism of nonlinear ultrasonic Lamb waves in thin plates with randomly distributed micro-cracks

Since the identification of micro-cracks in engineering materials is very valuable in understanding the initial and slight changes in mechanical properties of materials under complex working environments, numerical simulations on the propagation of the low frequency S₀ Lamb wave in thin plates with randomly distributed micro-cracks were performed to study the behavior of nonlinear Lamb waves. The results showed that while the influence of the randomly distributed micro-cracks on the phase velocity of the low frequency S₀ fundamental waves could be neglected, significant ultrasonic nonlinear effects caused by the randomly distributed micro-cracks was discovered, which mainly presented as a second harmonic generation. By using a Monte Carlo simulation method, we found that the acoustic nonlinear parameter increased linearly with the micro-crack density and the size of micro-crack zone, and it was also related to the excitation frequency and friction coefficient of the micro-crack surfaces. In addition, it was found that the nonlinear effect of waves reflected by the micro-cracks was more noticeable than that of the transmitted waves. This study theoretically reveals that the low frequency S₀ mode of Lamb waves can be used as the fundamental waves to quantitatively identify micro-cracks in thin plates.