Route to localising elastic energy via the topological rainbow effect

We combine three different fields, topological physics, metamaterials and elasticity to design a topological metasurface to control and redirect elastic waves. We strategically design a two-dimensional crystalline perforated elastic plate, that hosts symmetry-induced topological edge states. By concurrently allowing the elastic substrate to spatially vary in depth, we are able to convert the incident flexural wave into a series of robust modes, with differing envelope modulations. This adiabatic transition localises the incoming elastic energy into a concentrated region where it can then be damped or extracted. This elastic "topological rainbow" effect leverages two main concepts, namely the quantum valley-Hall effect and the rainbow effect usually associated with electromagnetic metamaterials. Due to the directional tunability of the elastic energy by geometry, our results have far-reaching implications for mechanical vibration applications such as switches, filters and energy-harvesters.