Nonlinear generation of negative-group-velocity Lamb waves by non-collinear mixing: Numerical and experimental investigations

Nonlinear guided-wave mixing in elastic plates with material nonlinearity, which produces scattered waves at sum and difference frequencies, has attracted significant attention for the nondestructive evaluation of early-stage damage. In previous theoretical studies, the possibility of generating negative-group-velocity Lamb waves by non-collinear mixing was indicated by perturbation analysis. This prediction was verified numerically and experimentally in the present study. In accordance with the prior theoretical framework, specific frequency pairs and intersection angles for two primary fundamental antisymmetric A0 Lamb waves were selected to produce observable negative-group-velocity S2b and positive-group-velocity S1 symmetric modes as scattered waves at a fixed sum frequency. The actual nonlinear generation of these scattered modes was confirmed through direct three-dimensional dynamic finite-element simulations and experimental measurements using an aluminum-alloy plate. In particular, it was demonstrated that the dominant scattered mode can be selectively switched between the S2b and S1 modes, with distinct propagation directions from the mixing region, by changing the primary frequencies while maintaining a constant intersection angle. Furthermore, an examination of the relationship between the scattered-wave amplitudes and the intersection angle for a given primary-frequency pair revealed that both modes exhibit their maximum amplitudes near the angles satisfying the theoretically derived resonance condition. These findings substantiate the earlier theoretical predictions and highlight the capability for adaptive manipulation of the scattered-wave propagation direction, an advantage unique to dispersive guided waves and absent in non-dispersive bulk waves.