A Lumped Model for Rotational Modes in Phononic Crystals

TL;DR

This paper introduces a simplified lumped model for understanding rotational modes in 2D phononic crystals, revealing their impact on band structure and predicting a novel Dirac-like cone at the Brillouin center.

Contribution

The paper develops a lumped model that explains rotational modes and predicts a new Dirac-like cone resulting from mode degeneracy in phononic crystals.

Findings

The model accurately reproduces dispersion relations.

It predicts a new Dirac-like cone at the Brillouin center.

Rotational motion significantly influences band structure.

Abstract

We present a lumped model for the rotational modes induced by the rotational motion of individual scatterers in two-dimensional phononic crystals comprised of square arrays of solid cylindrical scatterers in solid hosts. The model provides a physical interpretation of the origin of the rotational modes, reveals the important role played by the rotational motion in the band structure, and reproduces the dispersion relations. The model increases the possibilities of wave manipulation in phononic crystals. In particular, expressions, derived from the model, for eigen-frequencies at high symmetry points unambiguously predict the presence of a new type of Dirac-like cone at the Brillouin center, which is found to be the result of accidental degeneracy of the rotational and dipolar modes.