# Elastic wave control beyond band-gaps: shaping the flow of waves in plates and half-spaces

## TL;DR

This paper explores how to control elastic wave propagation beyond traditional band-gap limitations by tuning metasurface parameters, enabling versatile wave shaping in plates and half-spaces across various scales.

## Contribution

It demonstrates a method to engineer elastic wave flow using metasurfaces with tunable parameters, expanding control capabilities beyond conventional band-gap effects.

## Key findings

- Tuning rod height affects band-gap frequency and wave speed.
- Adjusting cluster periodicity influences dynamic anisotropy.
- Designs enable control of flexural and Rayleigh waves across scales.

## Abstract

It is well known in metamaterials that local resonance and hybridization phenomena dramatically influence the shape of dispersion curves; the metasurface created by a cluster of resonators, subwavelength rods, atop an elastic surface being an exemplar with these features. On this metasurface, band-gaps, slow or fast waves, negative refraction and dynamic anisotropy can all be observed by exploring frequencies and wavenumbers from the Floquet-Bloch problem and by using the Brillouin zone. These extreme characteristics, when appropriately engineered, can be used to design and control the propagation of elastic waves along the metasurface. For the exemplar we consider, two parameters are easily tuned: rod height and cluster periodicity. The height is directly related to the band-gap frequency, and hence to the slow and fast waves, while the periodicity is related to the appearance of dynamic anisotropy. Playing with these two parameters generates a gallery of metasurface designs to control the propagation of both flexural waves in plates and surface Rayleigh waves for half-spaces. Scalability with respect to the frequency and wavelength of the governing physical laws allows the application of these concepts in very different fields and over a wide range of lengthscales.