Design and sound absorption analysis of labyrinthine acoustic metamaterials based on fractal theory

Acoustic metamaterials exhibit exceptional sound absorption capabilities. This study introduces a fractal labyrinthine acoustic metamaterial (FLAM) designed for sound absorption analyses in a low-frequency range of 1–2000 Hz. The fractal curve is constructed through side substitution on an isosceles right triangle, which is chosen as the spatial recursive substructure due to its self-similarity. The FLAM model is then developed. With the thermal viscous losses considered in narrow channels, the sound absorption coefficient of this model is theoretically analyzed as the structural parameters significantly affect the sound absorption. A comprehensive analysis of low-frequency sound absorption performance is conducted for the first three orders, and the reconstruction of the structure with different combinations of fractal orders is examined to optimize the FLAM. The results show that the proposed FLAM achieves nearly perfect absorption in the 50–400 Hz range, with peak absorption coefficients of 0.99, 0.95, and 0.95 for the first three orders. The proposed FLAMs for the first three orders have total thicknesses of $0.032\lambda$, $0.021\lambda$, and $0.019\lambda$, demonstrating excellent low-frequency sound absorption at deep sub-wavelength scales.