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

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.

After discussion, it appears that the derivation condition derived in Eq. (2.7) page 3 does not seem to take into account resonance phenomena in resonators