Reflection and transmission of transient ultrasonic wave in fractal porous material: Application of fractional calculus

Zine El Abiddine Fellah (1) , M. Fellah (2) , E. Ogam (1) , A. Berbiche (2) , C. Depollier (3)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 USTHB - Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]
3 LAUM - Laboratoire d'Acoustique de l'Université du Mans

This paper provides a time domain model for the propagation of transient ultrasonic waves in a self-similar porous material having a rigid frame. This model is based on the formalism of Stillinger-Palmer-Stavrinou, which consists in modeling the fractal material as a porous medium with a non-integer dimensional space. This paper is devoted to the time-domain analytical calculus of the reection and transmission operators that are expressed in terms of Mittag-Leer functions. A sensitivity numerical study using ultrasonic reected and transmitted waves is performed, highlighting the eect of of the material's physical parameters (fractal dimension, tortuosity, viscous characteristic length and porosity) on the waveforms.

Mots clés: Fractional calculus; Fractal; Porous materials; Mittag-Leffler functions; Non-integer space dimension; Reflection and transmission

Domaines: Acoustique [physics.class-ph]

Zine El Abiddine Fellah, M. Fellah, E. Ogam, A. Berbiche, C. Depollier. Reflection and transmission of transient ultrasonic wave in fractal porous material: Application of fractional calculus. Wave Motion, 2021, 106, pp.102804. ⟨10.1016/j.wavemoti.2021.102804⟩. ⟨hal-03310651⟩