The effect of rheology with gas bubbles on linear elastic waves in fluid-saturated granular media

Ali, A. A. and Strunin, D. V. (2018) The effect of rheology with gas bubbles on linear elastic waves in fluid-saturated granular media. International Journal of Applied Mechanics and Engineering, 23 (3). pp. 575-594. ISSN 1734-4492

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Elastic waves in fluid-saturated granular media depend on the grain rheology, which can be complicated by the presence of gas bubbles. We investigated the effect of the bubble dynamics and their role in rheological scheme, 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 bubbles surrounded by the fluid. We derived the Nikolaevskiy-type equation describing the velocity of the solid matrix in the moving reference system. The equation is linearized to yield the decay rate λ as a function of the wave number k. We compared the λ(k)-dependence for the cases with and without the bubbles, using typical values of the input mechanical parameters. For both the cases, the λ(k) curve lies entirely below zero, which implies a global decay of the wave. We found that the increase of the radius of the bubbles leads to a faster decay, while the increase in the number of the bubbles leads to slower decay of the wave.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published version deposited according to an Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) License.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 17 Mar 2019 23:38
Last Modified: 05 Apr 2019 01:47
Uncontrolled Keywords: Frenkel-Biots waves, bubbles, rheology, porous media
Fields of Research : 01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.2478/ijame-2018-0031

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