On liners viscoacoustic impedance boundary conditions for an array of Helmholtz resonators in 3D

TL;DR

This paper develops a homogenized boundary condition model for a 3D array of Helmholtz resonators, simplifying the complex resonator interactions into an effective boundary condition using advanced asymptotic and homogenization techniques.

Contribution

It introduces a new limit model for resonator arrays that accounts for multi-scale effects, justified through rigorous asymptotic analysis and homogenization methods.

Findings

Derived an equivalent boundary condition for resonator arrays

Validated the model through asymptotic and homogenization analysis

Provides a rigorous mathematical justification for the limit model

Abstract

The present work deals with the resolution of the Linearized Navier-Stokes problem in a domain made of an array that consists into a repetition of elongated resonators connected to an half-space. We provide and justify a limit equivalent model which takes into account the presence of resonators array as an equivalent boundary condition. Our approach combines the method of matched asymptotic expansions and the method of periodic surface homogenization adapted to more than two scales, and a complete justification is included in the paper.