Microstructures for lowering the quarter wavelength resonance frequency of a hard-backed rigid-porous layer

The frequency of the quarter wavelength resonance in the sound absorption spectra due to a thin hard-backed rigid-porous layer can be influenced by the design of its microstructure as well as its thickness. Microstructures considered include parallel arrays of identical cylindrical, slit-like or rectangular pores with deep sub-wavelength cross sections inclined to the surface normal, cylindrical annular pores, slits with log-normal width distributions, slits with cross sections that vary in a sinusoidal manner and slits with two distinct widths (dual porosity). Formulae that predict the bulk acoustical properties due to these microstructures are presented and used to explore the extent to which specific microstructures could be used separately or in combination to improve low-frequency absorption. Predicted normal incidence absorption coefficient spectra are compared using microstructural dimensions that would be feasible for 3D printing. The most effective microstructures are predicted to be slits with sinusoidally-varying widths, or with two distinct widths, inclined to the surface normal at 70°. The quarter wavelength layer resonances predicted in absorption coefficient spectra using these microstructures are comparable with those predicted for layers of the same thickness and bulk porosity having cylindrical pores with dead-end branches.