Measurements of dynamic compressibility of air-filled porous sound-absorbing materials are compared with predictions involving two parameters, the static thermal permeability k 0 Ј and the thermal characteristic dimension ⌳Ј. Emphasis on the notion of dynamic and static thermal permeability-the latter being a geometrical parameter equal to the inverse trapping constant of the solid frame-is apparently new. The static thermal permeability plays, in the description of the thermal exchanges between frame and saturating fluid, a role similar to the viscous permeability in the description of the viscous forces. Using both parameters, a simple model is constructed for the dynamic thermal permeability kЈ(), which is completely analogous to the Johnson et al. ͓J. Fluid Mech. 176, 379 ͑1987͔͒ model of dynamic viscous permeability k(). The resultant modeling of dynamic compressibility provides predictions which are closer to the experimental results than the previously used simpler model where the compressibility is the same as in identical circular cross-sectional shaped pores, or distributions of slits, related to a given ⌳Ј.

No abstract

A new way of calculating the airflow resistivity of randomly placed parallel cylinders is presented. The calculation is based on Voronoi polygons, and the resistivity is given by the mean spacing between the fibers, their diameters, and the physical properties of air. New explicit formulas for the resistivity are given, which are valid for the cylinder ͑fiber͒ concentrations found in acoustic materials. A one-dimensional model consisting of parallel plates with random spacing between the plates is first discussed. Then a two-dimensional model consisting of parallel cylinders randomly spaced is treated for flow parallel and perpendicular to the cylinders. The resistivity formulas are exact for plates and approximate for cylinders.

The sound wave in the air between the fibers of glass wool exerts an oscillatory viscous drag on the fibers and excites a mechanical wave in the fiber skeleton. Accurate calculations of sound attenuation in glass wool must take the mechanical wave in the fiber skeleton into account, and this requires knowledge of the dynamic elastic constants of the fiber skeleton. The mechanical properties of glass wool are highly anisotropic. Previously only one of the elastic constants has been measured dynamically, but here all the elastic constants are reported. The measurement method is well known. But a new mechanical design, which reduces mechanical resonance, is described. The measurements were carried out in atmospheric air at normal pressure, and this causes an oscillatory airflow in the sample. To obtain the elastic constants, the influence of the airflow was subtracted from the data by a new formula. The elastic constants were measured in the frequency range 20-160 Hz for glass wool of mass density 30 kg/ m 3 . The elastic constant C 11 depended on the frequency; at 20 Hz it was 1.5+ 0.01i MPa, and at 160 Hz it was 2.6+ 0.06i MPa. The constant C 33 = 12+ 0.6i kPa did not depend on frequency. The shear constant C 44 =40+2i kPa was constant. The two constants C 12 , C 13 were zero.

The acoustic attenuation of acoustic fiber materials is mainly determined by the dynamic resistivity to an oscillating air flow. The dynamic resistance is calculated for a model with geometry close to the geometry of real fiber material. The model consists of parallel cylinders placed randomly. Two cases are treated: flow perpendicular to the cylinder axes, and flow parallel to the axes. In each case two new approximate procedures were used. In the first procedure, one solves the equation of flow in a Voronoi cell around the fiber, and averages over the distribution of the Voronoi cells. The second procedure is an extension to oscillating air flow of the Brinkman self-consistent procedure for dc flow. The procedures are valid for volume concentration of cylinders less than 0.1. The calculations show that for the density of fibers of interest for acoustic fiber materials the simple self-consistent procedure gives the same results as the more complicated procedure based on average over Voronoi cells. Graphs of the dynamic resistivity versus frequency are given for fiber densities and diameters typical for acoustic fiber materials.