The symmetric zero-frequency mode induced by weak material nonlinearity during Lamb wave propagation is explored for the first time. We theoretically confirm that, unlike the second harmonic, phase-velocity matching is not required to generate the zero-frequency mode and its signal is stronger than those of the nonlinear harmonics conventionally used, for example, the second harmonic. Experimental and numerical verifications of this theoretical analysis are conducted for the primary S₀ mode wave propagating in an aluminum plate. The existence of a symmetric zero-frequency mode is of great significance, probably triggering a revolutionary progress in the field of non-destructive evaluation and structural health monitoring of the early-stage material nonlinearity based on the ultrasonic Lamb waves.

We report a novel approach to control the wavefronts of shear vertical (SV) waves in solids using metasurfaces constituted by a stacked array of composite plates, which are composed of two connecting parts made of different materials. The metasurfaces are connected at two ends to the half-space solids where the elastic SV waves propagate. The incident SV waves in the left half-space solid induce flexural waves in the composite plates and subsequently are converted back to SV waves in the right half-space solid. The time delay of flexural waves in each composite plate of the metasurfaces is tuned through the varying length of the two connecting components. To quantitatively evaluate the time delay in each composite plate, a theoretical model for analyzing the phase of the transmitted SV waves is developed based on the Mindlin plate theory. To control the SV waves at will, each composite plate in the metasurface is delicately designed according to the proposed theoretical model. For illustrative purposes, two metasurfaces are designed and numerically validated.

This paper investigates the propagation of low-frequency S₀ mode Lamb waves in plates with quadratic nonlinearity through numerical simulations and experimental measurements. Both numerical and experimental results manifest distinct ultrasonic nonlinear behavior which is mainly presented by the second harmonics. Meanwhile, we find that both the acoustic nonlinearity parameter and dispersion distance show the exponential decay trend with the increase of frequency-thickness. Moreover, the results reveal that the frequency is key to affect the acoustic nonlinearity parameter and dispersion distance with the same frequency-thickness. This study theoretically and experimentally reveals that nonlinear Lamb waves of the low-frequency S₀ mode are feasible to quantitatively identify material weak nonlinearity in plates.