Negative refraction and mode trapping of flexural–torsional waves in elastic lattices

We consider the propagation of flexural and torsional waves in a square lattice of Euler–Bernoulli beams. The refraction and reflection of waves across interfaces between two dissimilar lattices is investigated. By carefully controlling the inertial and elastic properties of the lattice elements, we demonstrate that it is possible to induce negative refraction and other associated phenomena. These effects are shown to be broadband and are facilitated by the unprecedented control over wave propagation afforded by the interaction between torsional and flexural waves and the additional freedom associated with the applied forcing. Closed-form analytical findings are accompanied by numerical simulations, which demonstrate negative refraction, unidirectional reflection and mode trapping. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’.