New empirical equations for sound propagation in rigid frame fibrous materials

Abstract

New expressions are given that can be used instead of the phenomenological equations of Delany and Bazley. They provide similar predictions in the range of validity of these equations, and in addition are valid at low frequencies where the equations of Delany and Bazley provide unphysical predictions. These new expressions have been worked out by using the general frequency dependence of the viscous forces in porous materials proposed by Johnson et al. [J. Fluid Mech. 176, 379 (1987)], with a transposition carried out to predict the dynamic bulk modulus of air. The model used suggests how sound propagation in fibrous materials can depend both on the diameter of the fibers and on the density of the material.

Coherent and Incoherent Scattering Mechanisms in Air-Filled Permeable Materials

“…In the propagating region, the velocity depends on the tortuosity only while the attenuation coefficient is predicted to decrease with increasing permeability. Generally, the experimentally observed propagation parameters are consistent with existing theoretical models [5][6][7][8] except for an anomalous excess attenuation at very high frequencies. The excess high-frequency attenuation could be additional absorption due to increased viscous friction caused by the irregularity of the pore channels or geometrical scattering due to phase cancellation between rays propagating through various channels depending of the material properties [4].…”

Three-dimensional reconstruction of a random fibrous medium: Geometry, transport, and sound absorbing properties

“…2 In particular, we checked whether the thermal permeability k 0 0 and the viscous permeability were linked by…”

“…These systems usually exhibit interesting sound absorbing properties and are, in some respects, widely used in the transportation and building industries. While several studies have devoted considerable attention to the description of the acoustical characteristics of fibrous absorbents, [1][2][3][4] our understanding of the basic relationships between the structure and the acoustical properties of these fibrous webs is still to benefit from a better understanding. It would be particularly valuable to have a manageable set of geometrical parameters of the three-dimensional (3D) fiber web morphology, in terms of which the transport (e.g., static viscous k 0 and thermal k 0 0 permeabilities, viscous characteristic length K, high frequency tortuosity a 1 ) and acoustical properties of non-woven fibrous media could be described.…”

Asymptotic and exact fundamental solutions in hereditary media with singular memory kernels

“…In Biot's poroelasticity [5], G0o(t, x) = pi pfI pfl N(r, x) (2.8) where I denotes the 3x3 unit matrix and the viscodynamic operator N(r, x), explicitly known for some idealized pore geometries, has a singularity ~ r-1'2 [5,36,4,53,7,2,56]. The singularity of the viscodynamic operator is important for frequencies w > wb 1 0r,Hz, where wb denotes Biot's frequency.…”