Sound propagation in porous materials with annular pores

Abstract

Long-wavelength sound propagation in porous materials with annular pores is investigated in this paper. Closed-form analytical expressions for the effective acoustical properties of this type of material were obtained. These are compared with both direct numerical calculations of the effective properties and their calculations obtained by using semi-phenomenological models. Analytical expressions for the input parameters of the latter, i.e., static viscous and thermal permeabilities, viscous and thermal characteristic lengths, and tortuosity, are also provided. The introduced model is successfully validated by comparing its predictions with measured data taken from literature. A parametric analysis that allows highlighting the influence of the different geometrical parameters of porous materials with annular pores on their sound absorptive properties is also presented.

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

“…It has been shown analytically [3,5] that the complex density function, H(λ), for rectangular pores with sides 2a and 2b (see Table 1) reduces to that for slit pores of width 2b as a → ∞. Figure 3 indicates that predicted rectangular and slit-pore absorption coefficient spectra are numerically identical when a ≥ 4b.…”

“…Exact equations for a cylindrical annular pore involve cylindrical Bessel functions, as do those for an open cylindrical pore [3]. However, it has been shown [3] that, a semi-phenomenological model for an arbitrary pore microstructure, the Johnson-Champoux-Allard-Lafarge (JCAL) model [11,12], enables sufficiently accurate predictions of the acoustical properties of a layer containing cylindrical annular pores normal to the surface. In general, the JCAL model introduces viscous and thermal permeabilities, viscous and thermal characteristic lengths, porosity and tortuosity.…”

“…By using equation 4with equations (9) and (10), the original development [3] is extended to allow for inclination of annular pores to the surface normal.…”

“…Another deadend-pore microstructure design for a 0.035 m thick layer is predicted to give a narrow absorption coefficient peak with magnitude 0.65 at 0.65 kHz [2]. It has been found that hardbacked layers with cylindrical annular pores yield higher absorption than layers with the same thickness but with open cylindrical pores [3]. The measured absorption coefficient peak magnitude of 0.55 near 3.5 kHz for a 0.025 m thick sample containing 2 mm diameter cylindrical pores and with porosity 0.26 is increased to 0.95 near 3 kHz by inserting cylindrical rods into the open pores thereby creating annular pores of width 0.25 mm and reducing the bulk porosity to 0.11 [3].…”

“…The extended models are used to investigate the extent to which each form of microstructure either separately or in combination could be used to improve low-frequency absorption of a thin hard-backed layer. Numerical comparisons use microstructure dimensions on the order of those of metallic foams [1] or of those that have been used elsewhere [2][3][4][5]. The chosen dimensions are within the resolution of commonly-available 3D-printers (0.1 mm at present).…”