Harnessing Geometric Frustration to Form Band Gaps in Acoustic Channel Lattices

TL;DR

This paper shows that geometric frustration in 2D acoustic networks can create band gaps, enabling control over sound propagation, with potential applications in sound and vibration management.

Contribution

It introduces a novel mechanism using geometric frustration to generate acoustic band gaps in periodic networks, supported by numerical and experimental evidence.

Findings

Band gaps occur only in geometrically frustrated networks.

Resonant modes alone do not produce band gaps.

Geometric frustration enables new sound control methods.

Abstract

We demonstrate both numerically and experimentally that geometric frustration in two-dimensional periodic acoustic networks consisting of arrays of narrow air channels can be harnessed to form band gaps (ranges of frequency in which the waves cannot propagate in any direction through the system). While resonant standing wave modes and interferences are ubiquitous in all the analyzed network geometries, we show that they give rise to band gaps only in the geometrically frustrated ones (i.e. those comprising of triangles and pentagons). Our results not only reveal a new mechanism based on geometric frustration to suppress the propagation of pressure waves in specific frequency ranges, but also opens avenues for the design of a new generation of smart systems that control and manipulate sound and vibrations.