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Description
Thin layers of acoustic metamaterials can exhibit remarkable low-frequency sound absorption when their microstructures contain long, tortuous channels or coiled resonators. This is because the coiled, spiral or labyrinthine channels require a relatively small material thickness to significantly extend the path of oscillatory viscous flows induced by airborne acoustic waves that penetrate the air-saturated permeable material. From a homogenization perspective, these materials are characterised by exceptionally high tortuosity, which slows down acoustic waves. Test prototypes of such metamaterials with excellent acoustic properties can be easily produced using low-cost additive manufacturing techniques. However, experimental validation can exhibit deviations from model predictions, arising from elastic vibrations of the 3D-printed metamaterial structure. In this work, we use direct numerical simulations to show in which situations and how these effects occur. Furthermore, we demonstrate that the theory of permeo-elasticity provides a framework to capture these fluid-structure interaction effects and to determine the acoustic material performance by using a computationally more efficient approach based on unit-cell calculations. The proposed method based on this approach enables the informed and very efficient design of highly-tortuous permeo-elastic metamaterials, in which permeo-elastic effects enhance the desired low-frequency sound absorption. This method essentially involves designing a (printable) metamaterial structure that forms the walls of a tortuous channel and is flexible enough to exhibit elastic resonances in a desired frequency range between simultaneously designed quarter-wavelength resonances.