The role of rheology in modelling elastic waves with gas bubbles in granular fluid-saturated media

Ali, Adham A. and Strunin, Dmitry V. (2019) The role of rheology in modelling elastic waves with gas bubbles in granular fluid-saturated media. Journal of Mechanics of Materials and Structures, 14 (1). pp. 1-24. ISSN 1559-3959

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Abstract

Elastic waves in fluid-saturated granular media depend on the rheology which includes elements representing the fluid and, if necessary, gas bubbles. We investigated the effect of different rheological schemes, including and excluding the bubbles, on the linear Frenkel–Biot waves of P1 type. For the wave with the bubbles the scheme consists of three segments representing the solid continuum, fluid continuum, and a bubble surrounded by the fluid. We derived the Nikolaevskiy-type equations describing the velocity of the solid matrix in the moving reference system. The equations are linearized to yield the decay rate lambda as a function of the wave number k. We compared the lambda(k)-dependence for the cases with and without the bubbles, using typical values of the input mechanical parameters. For the both cases, the lambda(k)-curve lies entirely below zero, which is in line with the notion of the elastic wave being an
essentially passive system. We found that the increase of the radius of the bubbles leads to faster decay, while the increase in the number of the bubbles leads to slower decay of the elastic wave.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sept 2019 -)
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sept 2019 -)
Date Deposited: 31 Jan 2020 04:42
Last Modified: 09 Feb 2020 23:12
Uncontrolled Keywords: Frenkel–Biot’s waves, bubbles, rheology, porous media
Fields of Research : 04 Earth Sciences > 0404 Geophysics > 040407 Seismology and Seismic Exploration
01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970104 Expanding Knowledge in the Earth Sciences
Identification Number or DOI: 10.2140/jomms.2019.14.1
URI: http://eprints.usq.edu.au/id/eprint/37793

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