Low frequency, broadband and thin acoustic metamaterials for acoustic insulation

Elastic and locally resonant metamaterials can be used to improve the acoustic insulation properties of panels, particularly at low frequencies. Among the possible architectures, we are interested in the case of a very soft panel consisting of a porous material in which a periodic distribution of cylindrical inclusions is inserted. It has recently been established (JSV 571 (2024) 118005) that this configuration gives rise to a large and low-frequency transmission dip, explained by the coexistence of an elastic band gap and the destructive interference resulting from the interaction between an elastic resonance mode of the skeleton and a rigid body mode of the inclusions. The paper aims to describe the essential physical mechanisms involved in using a minimal lumped element model, the characteristics of which are extracted from the cell modes. The relevance of the minimal model is validated utilizing a comparison with reference results obtained using the finite element method. This approach focuses on the mechanisms involved and is not constrained by the choice of a particular geometric configuration (exact shape and size of the inclusion), allowing it to evolve.