The nonlinear interaction of Lamb waves has attracted considerable attention because of its potential for localizing micro-damage in plate-like structures. Most recent studies have focused on the nonlinear mixing of Lamb waves propagating in the same direction, but this makes it difficult to determine the exact position of micro-damage because of the relatively large mixing zone. To overcome these shortcomings, we consider the nonlinear interaction of counter-propagating Lamb waves in this letter. An obvious resonance phenomenon is first observed in both experiments and simulations, which agrees well with our previous theoretical analysis [Li et al., J. Appl. Phys. 124, 044901 (2018)]. Also, analyzing the time-domain signal shows that the precision of damage localization is a function of the frequencies, the number of cycles, and the phase and group velocities of the primary waves.

Nonlinear guided elastic waves have attracted extensive attention owing to their high sensitivity to microstructural changes. However, based on the widely used second harmonics, third harmonics and static components, it is still difficult to locate the micro-defects. Perhaps the nonlinear mixing of guided waves can solve these problems since their modes, frequencies and propagation direction can be flexibly selected. Note that the phenomena of phase mismatching usually occur due to the lack of precise acoustic properties for the measured samples, and they may affect the energy transmission from the fundamental waves to second-order harmonics as well as reduce the sensitivity to micro-damage. Therefore, these phenomena are systematically investigated to more accurately assessing the microstructural changes. It is theoretically, numerically, and experimentally found that the cumulative effect of difference- or sum-frequency components will be broken by the phase mismatching, accompanied by the appearance of the beat effect. Meanwhile, their spatial periodicity is inversely proportional to the wavenumber difference between fundamental waves and difference- or sum-frequency components. The sensitivity to micro-damage is compared between two typical mode triplets that approximately and exactly meet the resonance conditions, and the better one is utilized for assessing the accumulated plastic deformations in the thin plates.