The main purpose of this article is to present, within a unified framework, a technique based on numerical homogenization, to model the acoustical properties of real fibrous media from their geometrical characteristics and to compare numerical results with experimental data. The authors introduce a reconstruction procedure for a random fibrous medium and use it as a basis for the computation of its geometrical, transport, and sound absorbing properties. The previously ad hoc “fiber anisotropies” and “volume weighted average radii,” used to describe the experimental data on microstructure, are here measured using scanning electron microscopy. The authors show that these parameters, in conjunction with the bulk porosity, contribute to a precise description of the acoustical characteristics of fibrous absorbents. They also lead to an accurate prediction of transport parameters which can be used to predict acoustical properties. The computed values of the permeability and frequency-dependent sound absorption coefficient are successfully compared with permeability and impedance-tube measurements. The authors' results indicate the important effect of fiber orientation on flow properties associated with the different physical properties of fibrous materials. A direct link is provided between three-dimensional microstructure and the sound absorbing properties of non-woven fibrous materials, without the need for any empirical formulae or fitting parameters.
It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.
The purpose of this research is to determine whether the acoustic properties of polydisperse fibrous medium (PDFM) and bidisperse fibrous medium (BDFM) can be modeled by monodisperse fiber media (MDFM) with an effective fiber diameter. Multi-scale numerical simulations on representative elementary volumes of these media are performed to retrieve the transport and geometrical properties governing their acoustic properties. Results show no significant difference between predictions obtained by PDFM or BDFM, and their corresponding effective MDFM.
Poster SessionsLAMOX, the new family of oxide conductors, obtained on the basis of La2Mo2O9 compound with the use of different substitutions is the object for intensive studies. In 2005 year single crystals of the anionic conductor La2Mo2O9 were grown by crystallization from the nonstoichiometric flux [1]. Their polymorphism, domain structure and temperature dependences of conductivity and permittivity were studied [1]. Conductivity of these crystals at 750-600 C reaches 10 -1 -10 -2 Om -1 sm -1 . It was established that in dependence of the cooling rate and of the admixture content, these crystals can exist at the room temperature as stable monoclinic A-phase or metastable cubic B1-phase or as their mixture. Obtaining of the most complete and precise structural data about the crystals of cubic metastable B1phase from X-ray experiment was the purpose of the present study. It is important that these studies were done for the first time for single crystals. Cubic cell with a=7.158(1)Å, which was found for the studied single crystal, allowed to index about 84% of measured reflections. While solving the structure (in sp.gr. P213) it was established that La and Mo atoms are shifted from the threefold axes. Occupation of three positions of La and Mo atoms was found to be equal to 100%. Two of the three independent oxygen positions in this crystal are not fully occupied, have quite large thermal parameters and are located at the short distances from each other.
BODY:Abstract (200 words): The ability of fibrous media to mitigate sound waves is controlled by their transport properties that are themselves greatly affected by the geometrical characteristics of their microstructure such as porosity, fiber radius, and fiber orientation. Here, the influence of these geometrical characteristics on the anisotropic transport properties of random fiber structures is investigated. First, representative elementary volumes (REVs) of random fiber structures are generated for different triplets of porosity, fiber radius and fiber orientation. The fibers are allowed to overlap and are motionless (rigid-frame assumption). The fiber orientation is derived from a second order orientation tensor. Second, the transport equations are numerically solved on the REVs which are seen as periodic unit cells (PUCs). These solutions yield the transport properties governing the sound propagation and dissipation in the respective fibrous media. These transport properties are the tortuosity, the viscous and thermal static permeabilities, and the viscous characteristic length. Finally, relations are proposed to estimate the transport properties and the thermal characteristic length when the geometry of the fiber structures is known.
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