Acoustic transmission loss in Hilbert fractal metamaterials

Acoustic metamaterials are increasingly being considered as a viable technology for sound insulation. Fractal patterns constitute a potentially groundbreaking architecture for acoustic metamaterials. We describe in this work the behaviour of the transmission loss of Hilbert fractal metamaterials used for sound control purposes. The transmission loss of 3D printed metamaterials with Hilbert fractal patterns related to configurations from the zeroth to the fourth order is investigated here using impedance tube tests and Finite Element models. We evaluate, in particular, the impact of the equivalent porosity and the relative size of the cavity of the fractal pattern versus the overall dimensions of the metamaterial unit. We also provide an analytical formulation that relates the acoustic cavity resonances in the fractal patterns and the frequencies associated with the maxima of the transmission losses, providing opportunities to tune the sound insulation properties through control of the fractal architecture.