Simultaneous acoustic perfect absorption and rainbow trapping via topologically optimized sub-wavelength multi-slit sonic crystal metamaterials

Acoustic perfect absorption at 500 Hz and across the low-frequency range of 400–1000 Hz is demonstrated using a metamaterial structure composed of graded sub-wavelength multi-slit sonic crystal (MSSC) elements designed through a topology optimization framework that integrates a genetic algorithm with a novel effective medium approach, rigorously accounting for visco-thermal losses in the slits via Stinson’s model, avoiding reliance on artificial loss factors. The effective impedances of the unit cells embedding each MSSC element are precisely tuned to match the surrounding medium, thereby satisfying the critical coupling condition for optimal absorption. Remarkably, the optimized structure exhibits spatially graded acoustic properties that sequentially localize energy at designated frequencies, producing the rainbow-trapping phenomenon. Notably, the largest element measures only 7 cm in diameter—deeply sub-wavelength at about 1/12 the wavelength at 400 Hz. The proposed design and methodology offer promising applications in acoustic filtering, energy harvesting, and noise mitigation, particularly in ventilation systems.