Acoustic materials based on the Gosper curve

In this work, slotted acoustic materials based on a space filling curve called the Peano-Gosper curve are proposed and investigated. The slits in such materials form a complex pattern because they are divided by walls built along lines generated by the Gosper curve algorithm. The pattern can be twisted around an axis normal to its surface to increase the tortuosity inside the material, and therefore, modify its acoustic properties, which can be controlled by the turning angle or pitch of the twist. A highly efficient semi-analytical model has been developed to accurately predict the acoustic properties, in particular the sound absorption of such materials. It only requires a representative part of the pattern, or better, scanning the surface of the fabricated material so that the actual geometry and dimensions (in particular slit widths) are well reproduced in a two-dimensional finite element mesh generated on a representative fluid domain. The mesh is used to solve a dedicated Poisson problem and determine a few key parameters, and the rest of the modelling is based on analytical formulas. Material samples with straight and twisted slit patterns were 3D printed and then measured in an impedance tube to confirm semi-analytical sound absorption predictions.