Homogenization of an array of resonators of the Helmholtz type

We present a homogenization method based on two scale matched asymptotic expansion techniques for arrays of Helmholtz resonators. In the resulting effective model, the array is replaced by a homogeneous and anisotropic medium accounting for the cavities of the resonators while jump conditions apply across a fictitious interface accounting for the necks of the resonators. We show that the model is able to describe accurately resonators open with necks at both extremities (termed two-sided) or open at a single extremity (termed one-sided). In these two cases, the effect of the array spacing is exemplified, which allows (i) to tune the resonance of perfect transmission in the former case and (ii) to realize perfect absorption in the later case.