The multi-physics metawedge: graded arrays on fluid-loaded elastic plates and the mechanical analogues of rainbow trapping and mode conversion

We consider the propagation and mode conversion of flexural-acoustic waves along a fluid-loaded graded array of elastic resonators, forming a metasurface. The multi-physics nature of the problem, coupling two disparate physical systems, brings both challenges and novel features not previously seen in so-called bifunctional metamaterials. In particular, by using an appropriately designed graded array of resonators, we show that it is possible to employ our metasurface to mode-convert sub-sonic surface flexural waves into bulk acoustic waves and vice-versa; transferring energy between two very different physical systems. Whilst the sub-sonic mechanical surface wave is dispersive, the bulk acoustic wave is dispersionless and radiates energy at infinity. We also show that this bifunctional metasurface is capable of exhibiting the classical effect of rainbow trapping for sub-sonic surface waves.