On the dynamic viscous permeability tensor symmetry

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...

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Bibliographic Details
Published in:The Journal of the Acoustical Society of America 2008-10, Vol.124 (4), p.EL210-EL217
Main Authors: Perrot, Camille, Chevillotte, Fabien, Panneton, Raymond, Allard, Jean-François, Lafarge, Denis
Format: Article
Language:English
Subjects:
Acoustics
Architectural acoustics
Computer Simulation
Engineering Sciences
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mechanics
Models, Theoretical
Motion
Noise: its effects and control
Permeability
Physics
Porosity
Rheology
Time Factors
Viscosity
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Summary: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.
ISSN:0001-4966
1520-8524
DOI:10.1121/1.2968300