Sierpiński carpet-inspired hierarchical patterning of porous materials for sound absorption

Efficient sound absorption at low and mid frequencies is essential for mitigating anthropogenic noise but remains a scientific and engineering challenge. While porous materials are effective at medium and high frequencies, they typically require considerable thickness to absorb low-frequency sound. Inspired by the Sierpiński carpet, we propose a hierarchical pattern of through-thickness holes in porous materials to enhance low- and mid-frequency absorption. Numerical simulations and impedance tube measurements demonstrate significant performance gains (up to a 46% of improvement in absorption at 500 Hz using 10% less material for a thickness of 80 mm). This enhancement is attributed to the presence of small-scale geometric features that spatially localize the acoustic pressure field, increasing energy dissipation within the porous medium. This hierarchical approach holds promise for developing lightweight, high-performance panels for sound insulation applications, particularly where improved low- and mid-frequency absorption is required without increasing material bulk.