Low-frequency broadband sound absorption based on Cantor fractal porosity

Abstract

Proposals for new absorber designs for broadband sound absorption are of great interest due to their wide applicability in sound energy control. In this sense, the behavior of an acoustic absorber composed of a panel with slit-type perforations based on Cantor’s fractal is presented. The analytical model for the fractal porosity of the absorber as a function of the initial geometric parameters, the number of iterations, and the fractal dimension was established. The behavior of broadband sound absorption was evaluated theoretically, numerically, and experimentally, in which the predominant total thermal-viscous dissipation in the region of perforations increases as the fractal porosity of the absorber decreases. Furthermore, an experimental broadband sound absorption of 692 Hz (from 382 to 1074 Hz) with a peak amplitude greater than 80% is obtained with the proposed structure presenting a sub-wavelength scale, i.e., λ/27. Finally, this work contributes to the understanding of the use of Cantor’s fractal porosity in the proposal of new absorbers that allow broadband sound absorption at low frequency.