Analytical modeling of one-dimensional resonant asymmetric and reciprocal acoustic structures as Willis materials

Jean-Philippe Groby,Aurélien Merkel,Vicente Romero-García,Jensen Li,Vincent Tournat,Matthieu Malléjac,Daniel Torrent

doi:10.1088/1367-2630/abfab0

Abstract

As building blocks of acoustic metamaterials, resonant scatterers have demonstrated their ability to modulate the effective fluid parameters, which subsequently possess extreme properties such as negative bulk modulus or negative mass density. Promising applications have been shown such as extraordinary absorption, focusing, and abnormal refraction for instance. However, acoustic waves can be further controlled in Willis materials by harnessing the coupling parameters. In this work, we derive the closed forms of the effective parameters from the transfer matrix in three asymmetric and reciprocal one-dimensional resonant configurations and exhibit the differences in terms of coupling coefficients. The way in which Willis coupling occurs in spatially asymmetric unit cells is highlighted. In addition, the analysis shows the absence of odd Willis coupling for reciprocal configurations. These effective parameters are validated against experimental and numerical results in the three configurations. This article paves the way of a novel physical understanding and engineering use of Willis acoustic materials.

Highlights

Since the seminal work of Willis in the 80’s [1], the eponymous materials have received an increasing attention, because of their analogy with bi-isotropic electromagnetic metamaterials [2]
Most of the works to date have focused on the experimental evidence [4, 9, 10], physical origins [11], calculation [12,13,14], and enhancement [15] of Willis coupling, only a few have focused on deriving a closed form of these parameters
We focus on three resonant, asymmetric, and reciprocal one-dimensional unit cells and derive closed forms of the corresponding Willis coupling parameters, exhibiting different forms depending on the nature of the asymmetry

Summary

14 May 2021

Jean-Philippe Groby1,∗ , Matthieu Mallejac , Aurelien Merkel, Vicente Romero-García , Vincent Tournat, Daniel Torrent and Jensen Li4. China ∗ Author to whom any correspondence should be addressed

Introduction

Derivation of the Willis coupling parameters

Unit cell composed of a duct loaded by two detuned Helmholtz resonators

Unit cell composed of a duct with detuned clamped plates

Experimental validation of the effective parameters and discussion

Conclusion