Effective Phononic Crystals for Non-Cartesian Elastic Wave Propagation

TL;DR

This paper introduces effective phononic crystals that leverage periodicity and material property variation to control elastic wave propagation, enabling band gap creation and topologically protected modes in non-Cartesian geometries.

Contribution

It presents a novel approach to designing phononic crystals with non-Cartesian symmetry, expanding control over elastic waves beyond traditional Cartesian-based structures.

Findings

Demonstration of band gaps in cylindrically propagating waves

Identification of topologically protected interface modes

Realization of Cartesian phononic behaviors in near-source regions

Abstract

We introduce the concept of effective phononic crystals, which combine periodicity with varying isotropic material properties to force periodic coefficients in the elastic equations of motion in a non-Cartesian basis. Periodic coefficients allow for band structure calculation using Bloch theorem. Using the band structure, we demonstrate band gaps and topologically protected interface modes can be obtained in cylindrically propagating waves. Through effective phononic crystals, we show how behaviors of Cartesian phononic crystals can be realized in regions close to sources, where near field effects are non-negligible.