Trapped Modes and Negative Refraction in a Locally Resonant Metamaterial: Transient Insights into Manufacturing Bounds for Ultrasonic Applications

The transient scattering of in-plane elastic waves from a finite-sized periodic structure, comprising a regular grid of Swiss-cross holes arranged according to a square lattice, is considered. The theoretical and numerical modelling focuses on the unexplored ultrasonic frequency regime, well beyond the first, wide, locally resonant band-gap of the structure. Dispersive properties of the periodic array, determined by Bloch–Floquet analysis, are used to identify candidates for high-fidelity GPU-accelerated transient scattering simulations. Several unusual wave phenomena are identified from the simulations, including negative refraction, focusing, partial cloaking, and wave trapping. The transient finite element modelling framework offers insights on the lifetimes of such phenomena for potential practical applications. In addition, nonideal counterparts with rough edges are modelled using characteristic statistical parameters commonly observed in additive manufacturing. The analysis shows that the identified wave effects appear likely to be robust with respect to potential manufacturing uncertainties in future studies.