A0 mode Lamb wave propagation in a nonlinear medium and enhancement by topologically designed metasurfaces for material degradation monitoring

This paper intends to provide an application example of using metamaterials for elastic wave manipulation inside a nonlinear waveguide. The concept of phase-gradient metasurfaces, in the form of artificially architectured structures/materials, is adopted in nonlinear-guided-wave-based structural health monitoring (SHM) systems. Specifically, the second harmonic lowest-order antisymmetric Lamb waves (2nd A0 waves), generated by the mutual interaction between primary symmetric (S) mode and antisymmetric (A) mode waves, show great promise for local incipient damage monitoring. However, the mixing strength is adversely affected by the wave beam divergence, which compromises the 2nd A0 wave generation, especially in the far field. To tackle this problem, a metasurface is designed to tactically enhance the 2nd A0 waves through manipulating the phases and amplitudes of both primary waves simultaneously. After theoretically revealing the features of the 2nd A0 wave generation in a weakly nonlinear plate, an inverse-design strategy based on topology optimization is employed to tailor-make the phase gradient while ensuring the high transmission of the primary waves, thus converting the diverging cylindrical waves into quasi-plane waves. The efficacy of the design is tested in a 2nd-A0-wave-based SHM system for material degradation monitoring. Results confirm that the manipulated S and A mode waves can propagate in a quasi-planar waveform after passing the surface-mounted metasurface. Changes in material properties inside a local region of the host plate can be sensitively captured through examining the variation of the 2nd A0 wave amplitude. The concept presented here not only showcases the potential of metamaterial-enhanced 2nd A0 waves for material degradation monitoring, but also illuminates the promising direction of metamaterial-aided SHM applications in nonlinear waveguides.