Propagation of acoustic waves in porous media and their reflection and transmission at a pure-fluid/porous-medium permeable interface |
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| Authors: | A. Madeo S. Gavrilyuk |
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| Affiliation: | 1. Dip. di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma “La Sapienza”, via Scarpa 16, 00161 Rome, Italy;2. Aix-Marseille University, UMR CNRS 6595 IUSTI, 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France;3. Laboratorio di Strutture e Materiali Intelligenti, Fondazione Tullio Levi-Civita, Palazzo Caetani (Ala Nord), 04012 Cisterna di Latina (Lt), Italy;1. Department of Mathematics, Indira Gandhi University Meerpur, Rewari, 122503, India;2. Department of Mathematics, C.M.R.J Govt. College, Ellenabad, 125102, India;1. Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 61 avenue du Général de Gaulle, 94010, Créteil Cedex, France;2. Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5, boulevard Descartes 77454, Marne-la-Vallée Cedex 2, France;1. Inria Bordeaux Sud-Ouest, Team CARDAMOM, 200 rue Vieille Tour, 33405 Talence, France;2. Bordeaux INP, IMB, UMR 5251, F-33400, Talence, France;3. Institute of Mathematics & Computational Science, Zürich University, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland;1. School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo 454003, PR China;2. Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany;3. Univ Lille Nord de France, F-59000 Lille, France;4. UVHC, IEMN-DOAE, F-59313 Valenciennes Cedex 9, France;5. CNRS, UMR 8520, F-59650 Villeneuve d''Ascq, France;6. ERSITA, Faculté Polydisciplinaire d''Ouarzazate, Univ. Ibn Zohr, 45000 Ouarzazate, Morocco;7. LMTI, Faculté des Sciences d''Agadir, Université Ibn Zohr, BP 28/S Agadir, Morocco;1. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;2. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China |
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| Abstract: | We find a sufficient condition of hyperbolicity for a differential system governing the motion of a one-dimensional porous-medium, so ensuring the existence of a solution for the associated Cauchy problem. We study propagation of linear waves impacting at a pure-fluid/porous-medium interface and we deduce novel expressions for the reflection and transmission coefficients in terms of the spectral properties of the governing differential system. We show three-dimensional plots drawing reflection and transmission coefficients as functions of Biot’s parameters. In such a way we propose an indirect method for measuring Biot’s parameters when the measurement of the reflection and transmission coefficients associated to the traveling waves is possible. |
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