Effect of Hilbert Fractal Acoustic Metamaterials on Ventilation Noise Control

Abstract Ventilation noise control devices often involve a trade-off between their size and ventilating performance, which limits the ability to reduce low-frequency sound in high-ventilation conditions. To address this challenge, the present study explores the use of Hilbert fractal-based design in ventilated metamaterials for improved acoustic performance. The sound transmission loss (STL) of these metamaterials is compared to that of a simple expansion chamber, which serves as the base case. Various parameters, including Hilbert order (O), channel width (K), ventilated space (l), unit cell thickness (H), and the number of unit cells (N) are investigated. Initially, the transfer matrix method evaluates STL without considering thermoviscous effects, which are later incorporated in numerical simulations and impedance tube experiments. The parametric study reveals that increasing the Hilbert curve order decreases the fundamental frequency, while a higher K value increases it. Additionally, more unit cells enhance STL but reduce its broadband nature. Through the finite element method, band diagrams and eigenmodes of Hilbert and base configurations indicate that increased Hilbert orders result in more bands and correspondence between transmission loss spectra and band gaps. The study also identifies dipole resonance modes in the Hilbert structure, which induce a negative effective bulk modulus that contributes to STL. Real-time performance testing in a twin reverberation chamber demonstrates that the Hilbert structure achieves a 5-dB improvement in STL compared to the base configuration across the 700- to 1400-Hz range. These findings are essential for achieving broadband low-frequency noise reduction while allowing airflow.