Computational homogenisation of acoustic metafoams

M.A Lewińska,V.G Kouznetsova,J.A.W Van Dommelen,M.G.D Geers

doi:10.1016/j.euromechsol.2019.103805

M.A Lewińska, V.G Kouznetsova + Show 2 more

Open Access

https://doi.org/10.1016/j.euromechsol.2019.103805

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Abstract

Acoustic metafoams are novel materials recently proposed for low frequency sound attenuation. The design of their microstructure is based on the combination of standard acoustic foams with locally resonant acoustic metamaterials. This results in improved sound attenuation properties due to the interaction between viscothermal dissipation effects and the local resonance effects at the pore level. In this paper, the non-standard behaviour of such a metafoam with a complex two-phase microstructure is analysed through a multiscale approach. The macroscopic problem is described by general balance equations and at the microscopic scale a detailed representation of the microstructure is considered. The frequency dependent effective properties are used to explain the extraordinary acoustic performance. The homogenisation approach is also validated using direct numerical simulations, showing that the homogenisation technique is adequate in modelling both viscothermal dissipation and the local resonance effect within the metafoam microstructure.

Highlights

Low frequency sound attenuation in a subwavelength regime is a challenging task
Acoustic metafoams rely on the combination and interaction of two interplaying attenuation mechanisms, namely, the viscothermal dissipation occurring in standard acoustic foams and local resonance effects
In order to assess the applicability of the homogenisation framework to an acoustic metafoam, a cubic unit cell is considered, following

Summary

Introduction

Low frequency sound attenuation in a subwavelength regime is a challenging task. On one hand, the mass law dictates a heavy weight for a sound isolation barrier (Ballou, 2015), whereas on the other hand, in order to perturb or absorb the waves of long wavelengths, a large thickness of such a barrier is required (Long, 2005). A different approach towards the low frequency noise challenge has recently been presented in Lewińska et al (2019), where instead of designing a metastructure with an extraordinary behaviour, a new class of materials, acoustic metafoams, has been proposed. Acoustic metafoams rely on the combination and interaction of two interplaying attenuation mechanisms, namely, the viscothermal dissipation occurring in standard acoustic foams and local resonance effects. This combination results in enhanced wave absorption and reflection. The demonstration of this concept was based on a poro-elastic unit cell with an embedded resonating mass, where the numerical studies involved band structure analyses and transmission spectrum calculations. There is a strong need for an efficient computational approach to assess the performance of such materials in realistic finite size applications

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