Designing band gaps with randomly distributed sub-wavelength Helmholtz resonators

Abstract

It is well-known that band gaps for wave propagation, in the frequency domain, can be achieved by using periodically-arranged inclusions in a host material. However it has been challenging to design materials with broad band gaps or that have multiple overlapping band gaps. For periodic composites this difficulty arises because many different length scales would have to be repeated periodically within the same structure to have multiple overlapping band gaps. Here we present an alternative: to design band gaps with disordered materials. We show how to tailor band gaps by choosing any combination of Helmholtz resonators that are positioned randomly within a host acoustic medium. One key result is that, via analytical (asymptotic) analysis, we are able to derive simple formulae for the effective material properties, which work over a broad frequency range. These can therefore be used to rapidly design tailored metamaterials. We show that these formulae are robust by comparing them with high-fidelity Monte-Carlo simulations over randomly positioned resonant scatterers.

Metadata

Item Type:	Article
Authors/Creators:	Piva, P.S. https://orcid.org/0000-0002-8239-970X Gower, A.L. Abrahams, I.D.
Copyright, Publisher and Additional Information:	© The Author(s) 2026. Open Access: This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
Keywords:	Applied physics; Electronics, photonics and device physics; Statistical physics, thermodynamics and nonlinear dynamics; Theory and computation
Dates:	Accepted: 27 January 2026 Published (online): 3 March 2026 Published: 3 March 2026
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Engineering (Sheffield) > School of Mechanical, Aerospace and Civil Engineering
Date Deposited:	10 Mar 2026 15:48
Last Modified:	10 Mar 2026 15:48
Status:	Published
Publisher:	Springer Science and Business Media LLC
Refereed:	Yes
Identification Number:	10.1038/s44384-026-00045-w
Related URLs:	Dataset
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:238820