On the design of finite-size noise insulating metamaterials based on Helmholtz resonators

Abstract Acoustic metastructures are often considered promising alternatives to conventional noise-insulating systems. Experimental demonstrations of transmission properties of such structures are frequently performed under specific conditions of quasi-1D or quasi-2D systems, which might result in quantitative discrepancies between the predicted and measured transmission coefficients, as demonstrated in this work. An array of paired C-shaped Helmholtz resonators is considered as an example. It is shown that coupling between the resonators along the axis orthogonal to the direction of wave propagation leads to non-uniform field distributions contradicting Floquet periodicity conditions applied to the associated infinitely periodic structures. Therefore, not only the thickness but also the width of the structure should be taken into account, as it affects the depth and spectral width of stop-bands. These observations are expected to be helpful for re-evaluation of the approaches to the design of acoustic metastructures.