Energy localizations of flexural edge waves via deep-subwavelength metasurfaces

The manipulation of elastic waves of large wavelengths with a structure of small size has been a long-standing objective in the field of elastodynamics. Elastic metasurfaces offer a promising solution in the subwavelength range, with the potential for extension to the deep subwavelength range through the introduction of local resonances. Here, we present a kind of deep-subwavelength metasurface (DSMS), which is comprised of a cluster of mass-spring resonators, and achieve enhanced guidance and energy localization of flexural edge waves (FEWs). The local resonance of the resonators provides a strong coupling between resonators and a substrate, which leads to the guidance of flexural waves, that is, guided modes. From the point of view of dynamic stiffness, the guided modes emerge from the weak equivalent stiffness of area near the resonators: stronger coupling weaker equivalent stiffness. On the basis of these, we design two quasi-periodic DSMSs to realize different amplification of FEWs: rainbow reflection and topological interface state. This amplification can be achieved by simply constructing a one-dimensional array on a plate without structuring the entire plate like conventional metamaterials. Our work extends the concept and the design method of elastic metasurfaces and provides a new route to manipulate the energy distribution in an elastic thin plate, which may exhibit wide applications in energy harvesting and acoustic device development.