Transient wave propagation in inhomogeneous porous materials: application of fractional derivatives

Authors:
M. Fellah;Z. E. A. Fellah;C. Depollier
Affiliations:
Laboratoire de Physique Théorique, Institut de Physique, USTHB, Bab Ezzouar, Algéria;Laboratoire de Mécanique et d'Acoustique, Marseille, France;Laboratoire d'Acoustique de l'Université du Maine, Université du Maine, Le Mans Cedex, France
Venue:
Signal Processing - Fractional calculus applications in signals and systems
Year:
2006

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Abstract

Acoustic wave propagation in inhomogeneous porous material is studied in the time domain. Fractional calculus is used to describe the inertial, viscous and thermal interactions between fluid and structure. A generalized hyperbolic fractional equation (generalized Telegraph equation) for transient sound wave propagation in inhomogeneous material is established. A wave-splitting technique is presented formally for the description of the dynamic equation of the reflection scattering operator.