Sound absorption and reflection from a resonant metasurface: Homogenisation model with experimental validation

Olga Umnova,Logan Schwan,Claude Boutin

doi:10.1016/j.wavemoti.2017.02.004

Abstract

Efficient manipulation of sound waves by some resonant acoustic metasurface designs has recently been reported in the literature. This paper presents a general theoretical framework for the description of sound wave interaction with the resonant metasurface that is independent of the nature of resonators and the excitation. The equations governing the behaviour of the metasurface are upscaled from the rigorous description of its unit cell using the two scale asymptotic homogenisation. The procedure relies on the existence of the boundary layer confined in the vicinity of the resonators operating in the deep subwavelength regime. The model is capable of describing sound interaction with the array of resonators positioned above or upon the substrate, so that the out of plane direction becomes an additional degree of freedom in the design. It is shown that at the leading order, the behaviour of the resonant surface is described in terms of the effective admittance, whose unconventional properties makes it possible to achieve the total sound absorption at multiple frequencies, broadband absorption, the phase reversal of the reflected wave at resonance and the control of the enclosure modes. The theory is validated by experiments performed in the impedance tube and in the anechoic environment using a surface array of spherical Helmholtz resonators with the extended inner neck. Experimental results confirm the effectiveness and robustness of the resonant surface for control of sound waves.

Highlights

This article is devoted to the theoretical and experimental study of a resonant surface, that is a two-dimensional array of resonators arranged at a surface in a regular lattice
Under the condition of scale separation for both in-plane and out-ofplane characteristic lengths, the two-scale asymptotic homogenisation model, based on the fundamental principles applied to the local scale, is shown to successfully predict the macroscopic behaviour of resonant surfaces
Resonant surface effects are more related to the acoustic flux distribution the resonators create at the boundary than to their exact nature

Summary

Introduction

This article is devoted to the theoretical and experimental study of a resonant surface, that is a two-dimensional array of resonators arranged at a surface in a regular lattice. Both resonators and the spacing between them are small compared to the wavelength at the resonance frequency (condition of scale separation). Resonant surfaces are of interest in many domains of physics They can be used, for instance, to control wavefields through tunable boundary conditions [1,2,3], or to achieve the perfect absorption of an incident wave [4,5]. While resonant surfaces are usually effective in a narrow frequency range close to the resonance, the use of several mistuned resonators per period can broaden the working frequency range [9], but it complicates the design as the period has to remain small compared to the wavelength

Methods

Results

Conclusion