Noise attenuating performance of metasurfaces with regular Euclidean tiling and uniformly embedded Helmholtz resonators

Abstract

Sound-attenuation capabilities of a certain class of subwavelength sound barriers based on wall-embedded Helmholtz resonators and a ventilation duct are studied theoretically and numerically. A simple analytical expression for the broadband integral transmission attenuation is introduced for this type of metasurface structures, which indicates that the sound blocking performance depends only on the main operational frequency, thickness and ventilation capacity of the structure. This result derived from the lumped parameter theory implies that the trade-off between the barrier performance and its physical footprint is inevitable and provides a practical guidance for the design strategies with specific targets and limitations. Detailed finite element modelling (FEM) parameter study is performed both to validate the theoretical predictions and test the limitations of simple lumped parameter approach. It was found that the agreement between the analytical and finite element results is very good for the structure thickness greater than 30 mm in a 300–1000 Hz frequency range. However, at smaller thickness values the FE results start to diverge from the predictions and also become dependent on the specific cell shape, which suggests that more advanced analytical approach is required for thinner metasurfaces.