1. On the dynamic viscous permeability tensor symmetry
- Author
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Raymond Panneton, Camille Perrot, Jean-François Allard, Fabien Chevillotte, Denis Lafarge, INSA Lyon, LVA, Laboratoire Vibrations Acoustique (LVA), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA), Groupe d'Acoustique de l'Université de Sherbrooke (GAUS), Département de génie mécanique [Sherbrooke] (UdeS), Université de Sherbrooke (UdeS)-Université de Sherbrooke (UdeS), Laboratoire d'Acoustique de l'Université du Mans (LAUM), and Le Mans Université (UM)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Time Factors ,Acoustics and Ultrasonics ,Generalization ,Motion (geometry) ,Geometry ,02 engineering and technology ,Symmetry group ,01 natural sciences ,Permeability ,010305 fluids & plasmas ,Motion ,0203 mechanical engineering ,Arts and Humanities (miscellaneous) ,0103 physical sciences ,Convergence (routing) ,Perpendicular ,Hexagonal lattice ,Computer Simulation ,ComputingMilieux_MISCELLANEOUS ,Mathematics ,[SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph] ,Viscosity ,Mathematical analysis ,Acoustics ,Models, Theoretical ,Symmetry (physics) ,[PHYS.MECA.ACOU]Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph] ,020303 mechanical engineering & transports ,Aeroacoustics ,Rheology ,Porosity - Abstract
Copyright 2008 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.; International audience; Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and∕or convergence assessment.
- Published
- 2008