Transient Propagation of Longitudinal and Transverse Waves in Cancellous Bone: Application of Biot Theory and Fractional Calculus

Autor: Djihane Benmorsli, Zine El Abiddine Fellah, Djema Belgroune, Nicholas O. Ongwen, Erick Ogam, Claude Depollier, Mohamed Fellah
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Symmetry, Vol 14, Iss 10, p 1971 (2022)
Druh dokumentu: article
ISSN: 14101971
2073-8994
DOI: 10.3390/sym14101971
Popis: In this paper, the influence of the transverse wave on sound propagation in a porous medium with a flexible structure is considered. The study is carried out in the time domain using the modified Biot theory obtained by the symmetry of the Lagrangian (invariance by translation and rotation). The viscous exchanges between the fluid and the structure are described by fractional calculus. When a sound pulse arrives at normal incidence on a porous material with a flexible structure, the transverse waves interfere with the longitudinal waves during propagation because of the viscous interactions that appear between the fluid and the structure. By performing a calculation in the Laplace domain, the reflection and transmission operators are derived. Their time domain expressions depend on the Green functions of the longitudinal and transverse waves. In order to study the effects of the transverse wave on the transmitted longitudinal waves, numerical simulations of the transmitted waves in the time domain by varying the characteristic parameters of the medium are realized whether the transverse wave is considered or not.
Databáze: Directory of Open Access Journals
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