On the existence of the low-frequency surface waves in a porous medium

Inna Edelman

doi:10.1016/j.crme.2003.11.004

On the existence of the low-frequency surface waves in a porous medium

Presented by: Évariste Sanchez-Palencia

Inna Edelman ¹

¹ Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany

Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 43-49.

Abstract
Résumé

The existence and propagation of the surface waves at a vacuum/porous medium interface are investigated in the low frequency range. Two types of surface waves are shown to be possible: the generalized Rayleigh wave, which always exists, and the Stoneley wave, which exists for a limited range of wave numbers. Moreover, within the k-domain of existence the Stoneley wave cannot appear for certain values of elastic parameters of the solid phase. The bifurcation behavior of both the Stoneley wave and the Biot (P2) bulk wave, depending on the wave number, is revealed. The asymptotic formulas for the phase velocities of the surface waves are derived.

La nature et la propagation des ondes de surface engendrées par la surface libre d'un milieu poreux sont étudiées en basse fréquence : nous mettons en évidence deux types d'ondes de surface : l'onde de Rayleigh et l'onde de Stoneley. Cette dernière existe pour une gamme limitée de nombres d'onde. Le comportement de bifurcation de l'onde de Stoneley et de l'onde lente de Biot (P2) dépendant du nombre d'onde est mis en évidence. Il est aussi prouvé qu'à l'intérieur du domaine d'existence du nombre d'onde, l'onde de Stoneley ne peut pas apparaı̂tre pour certaines valeurs de paramètres élastiques de la phase solide. Les formules asymptotiques des vitesses de phase des ondes de surface sont également présentées.

Received: 2003-06-26
Accepted: 2003-11-21
Published online: 2003-12-21

DOI: 10.1016/j.crme.2003.11.004

Keywords: Porous media, Waves, Asymptotic analysis, Bifurcation, Interface
Mots-clés : Milieux poreux, Ondes, Analyse asymptotique, Bifurcation, Interface

Author's affiliations:

Inna Edelman ¹

¹ Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany

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Inna Edelman. On the existence of the low-frequency surface waves in a porous medium. Comptes Rendus. Mécanique, Volume 332 (2004) no. 1, pp. 43-49. doi : 10.1016/j.crme.2003.11.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.11.004/

References
Cited by

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[7] K. Wilmanski Lagrangean model of two-phase porous material, J. Non-Equilib. Thermodyn., Volume 20 (1995), pp. 50-77

[8] I. Edelman Bifurcation of the Biot slow wave in a porous medium, J. Acoust. Soc. Am., Volume 114 (2002) no. 1, pp. 90-97

[9] I. Edelman Waves on boundaries of porous media, Phys. Dokl., Volume 46 (2001), pp. 517-521

[10] I. Edelman, On the bifurcation of the Biot slow wave in a porous medium, WIAS, Preprint 738 (2002).²

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