Analytical Approximations for Sub Wavelength Sound Absorption by Porous Layers with Labyrinthine Slit Perforations

Abstract

Analytical approximations for the acoustical properties of a rigid-porous matrix perforated by labyrinthine slits are developed using classical theories for sound propagation in tortuous slits and for sound absorption by double porosity materials. Predictions of enhanced low-frequency absorption result from a combination of pressure diffusion and labyrinth tortuosity if there is a high permeability contrast between the matrix and the labyrinthine slit. Additional insight into the predicted influence of the properties of the porous matrix is gained by considering the matrix porosity to be provided by inclined micro-slits. Extra tortuosity can be introduced by alternating the width of the labyrinthine slit. An alternating-width vertical-wall labyrinth perforation is predicted to lead to low-frequency absorption peaks in a relatively low-flow-resistivity and low-porosity matrix. Example predictions, even when using underestimates of labyrinth tortuosity, demonstrate the potential of labyrinthine slit perforations for achieving narrowband deep sub wavelength absorption peaks from thin hard-backed porous layers.