Symmetry and resonant modes in platonic grating stacks

TL;DR

This paper investigates flexural wave modes in stacks of gratings with rigid pins, revealing how resonant interactions can be controlled for potential wave manipulation applications.

Contribution

It introduces a detailed analysis of symmetry-based mode classification and demonstrates a method to steer the EDIT phenomenon across frequencies and angles.

Findings

Resonant modes are classified into even and odd groups.

The EDIT phenomenon can be controlled by adjusting grating reflectance.

High quality factor resonances are achievable over a wide parameter range.

Abstract

We study the flexural wave modes existing in finite stacks of gratings containing rigid, zero-radius pins. We group the modes into even and odd classes, and derive dispersion equations for each. We study the recently discovered EDIT (elasto-dynamically inhibited transmission) phenomenon, and relate it to the occurrence of trapped waves of even and odd symmetries being simultaneously resonant. We show how the EDIT interaction may be steered over a wide range of frequencies and angles, using a strategy in which the single-grating reflectance is kept high, so enabling the quality factors of the even and odd resonances to be kept large.