Tilted resonators in a triangular elastic lattice: chirality, Bloch waves and negative refraction

TL;DR

This paper studies a triangular elastic lattice with tilted resonators, revealing how their orientation induces resonant modes, band gaps, and negative refraction, enabling novel wave control such as elastic lensing.

Contribution

It introduces the concept of tilted resonators in a triangular lattice, demonstrating their impact on wave dispersion, band gap formation, and negative refraction phenomena.

Findings

Tilted resonators create resonant modes in the Bloch spectrum.

Tilting induces band gaps at Dirac-like points.

Structured interfaces with tilted resonators enable negative refraction and focusing.

Abstract

We consider a vibrating triangular mass-truss lattice whose unit cell contains a resonator of a triangular shape. The resonators are connected to the triangular lattice by trusses. Each resonator is tilted, i.e. it is rotated with respect to the triangular lattice's unit cell through an angle $\vartheta_0$. This geometrical parameter is responsible for the emergence of a resonant mode in the Bloch spectrum for elastic waves and strongly affects the dispersive properties of the lattice. Additionally, the tilting angle $\vartheta_0$ triggers the opening of a band gap at a Dirac-like point. We provide a physical interpretation of these phenomena and discuss the dynamical implications on elastic Bloch waves. The dispersion properties are used to design a structured interface containing tilted resonators which exhibit negative refraction and focussing, as in a "flat elastic lens".