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

Experiments and numerical methods were used to investigate the key parameters which affect the transmission loss behaviour of Hilbert fractal acoustic metamaterials. The tests were conducted using a four-microphone impedance tube, and the numerical simulation was performed using COMSOL Multiphysics software. Fractal order and cavity slot widths on Hilbert fractal metamaterials were investigated. 3D printing manufacturing techniques were used to make polylactic acid specimens. The COMSOL model developed utilised thermo-viscous and lossless domains with boundary layer mesh in the fractal cavities. The tests and simulations' frequency range were 0.2 kHz to 3.0 kHz, with parametric gap widths ranging from 0.5 mm to 3.0 mm. There is a reasonable agreement between the numerical models and the experimental results; the second-order Hilbert fractal had the most significant effect on transmission loss, with an experimental peak of nearly 50 dB around 1600 Hz. Moreover, multiple transmission loss peaks were observed as a function of the gap width in the five Hilbert fractal orders studied. The gap width is one of the critical parameters for optimising the performance of the Hilbert fractal as an acoustic metamaterial.