Experimental and Numerical Studies on the Hilbert Fractal Architecture as an Acoustic Metamaterial

We evaluate via experiments and numerical methods the transmission loss behaviour of Hilbert Fractal Metamaterials (HFMs)s tested in a four-microphone impedance tube. We explore the effect of the fractal order and widths of the cavity slots of HFMs 3D printed in PLA polymer. The COMSOL Finite Element models used here consider both thermoviscous and lossless domains. Tests and simulations have been carried out between 0.2 kHz and 3.0 kHz, with gap widths parametrised between 0.5 mm and 3.0 mm. A broad agreement is observed between the numerical models and the experimental results. The Hilbert fractal with the highest impact in terms of transmission loss is the one represented by the second order, with an experimental peak of almost 50 dB around 1600 Hz. All the HFMs orders show the presence of multiple TL peaks, with the gap width also a critical parameter to tailor the performance of these metamaterials.