Spiral-based phononic plates: From wave beaming to topological insulators

TL;DR

This paper introduces spiral-based phononic plates that utilize simple, parametrized spirals to control elastic wave dispersion, enabling band gaps, wave beaming, and topological insulator behaviors in easily fabricated structures.

Contribution

It presents a novel design approach using spiral unit cells to achieve various wave control mechanisms, including band gaps and topological effects, in planar phononic materials.

Findings

Full band gaps achieved via Bragg scattering, local resonances, and inertial amplification.

Wave beaming effects created by altering unit cell symmetry and lattice vectors.

Topologically protected band gaps demonstrated in spiral-based phononic plates.

Abstract

Phononic crystals and metamaterials take advantage of pre-designed geometrical structures to sculpt elastic waves, controlling their dispersion using different mechanisms. These mechanisms revolve mostly around Bragg scattering (BS), local resonances (LR) and inertial amplification (IA), which employ ad-hoc, often problem-specific geometries. Here, we use parametrized, spiraling unit cells as building blocks for designing various types of phononic materials. We focus on planar spirals that are easy to fabricate, yet give rise to the desirable complex dynamics. By simple modifications of the spirals, we open full band gaps using BS, LR and IA. Moreover, we alter the underlying unit cell symmetry and lattice vectors, to create wave beaming and topologically protected band gaps, both affecting waves whose wavelength is much larger than the order of periodicity.