Graded-crown Helmholtz metamaterial panels for broadband low-frequency noise control

Persistent low-frequency noise in dense urban environments degrades sleep, cognition and speech privacy in both residential and commercial rooms. Conventional porous absorbers become impractically thick below 500 Hz, while single-mode resonators provide insufficient bandwidth. Acoustic metamaterials are periodic microstructures that can harness local resonances to tailor effective mass and bulk modulus which enables deep-sub-wavelength control at architecturally acceptable thicknesses. We present a slit-neck Helmholtz metamaterial capped by a graded modulation crown of quarter-wavelength side branches. The crown forms a composite neck that lowers the primary Helmholtz resonance and, through deliberate grading, cascades secondary quarter-wavelength modes to widen the bandgap. Two- and three-dimensional thermoviscous finite element analyses predict strong absorption below 500 Hz, with additional tunable quarter-wavelength resonances spanning 1–10 kHz. Free-field measurements of stereolithography printed specimens validate the model, confirming peak absorption coefficients up to 0.8. Further multiphysics simulations show that an optional porous lining can extend the effective side-branch length and smooth the absorption peaks. The square unit-cell footprint permits gap-free tiling on walls or ceilings, providing a lightweight, rigid and tunable platform for broadband low-frequency noise mitigation in urban interiors.