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

Article

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. https://doi.org/10.2140/jomms.2019.14.1
Article Title

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

ERA Journal ID36514
Article CategoryArticle
AuthorsAli, Adham A. (Author) and Strunin, Dmitry V. (Author)
Journal TitleJournal of Mechanics of Materials and Structures
Journal Citation14 (1), pp. 1-24
Number of Pages24
Year2019
Place of PublicationUnited States
ISSN1559-3959
Digital Object Identifier (DOI)https://doi.org/10.2140/jomms.2019.14.1
Web Address (URL)https://msp.org/jomms/2019/14-1/jomms-v14-n1-p01-p.pdf
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.

KeywordsFrenkel–Biot’s waves, bubbles, rheology, porous media
ANZSRC Field of Research 2020370609. Seismology and seismic exploration
490105. Dynamical systems in applications
490109. Theoretical and applied mechanics
Byline AffiliationsComputational Engineering and Science Research Centre
Institution of OriginUniversity of Southern Queensland
Permalink -

https://research.usq.edu.au/item/q58w0/the-role-of-rheology-in-modelling-elastic-waves-with-gas-bubbles-in-granular-fluid-saturated-media

Log in to edit

Download files

Accepted Version
Ali-Strunin-final-corrected-proofs.pdf
File access level: Anyone

  • 154
    total views
  • 152
    total downloads
  • 5
    views this month
  • 1
    downloads this month

Export as

Related outputs

Finding exact solutions for selected nonlinear evolution differential equations
Bhanot, Rajeev P., Mohammed, Mayada G.. and Strunin, Dmitry V.. 2023. "Finding exact solutions for selected nonlinear evolution differential equations." Journal of Interdisciplinary Mathematics. 26 (7), pp. 1461-1470. https://doi.org/10.47974/JIM-1566
Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers
Strunin, Dmitry V. and Malomed, Boris A.. 2023. "Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers." Physical Review E. 107 (6). https://doi.org/10.1103/PhysRevE.107.064203
An effective high-order five-point stencil, based on integrated-RBF approximations, for the first biharmonic equation and its applications in fluid dynamics
Mai-Duy, Nam, Tien, Cam Minh Tri, Strunin, Dmitry and Karunasena, Karu. 2023. "An effective high-order five-point stencil, based on integrated-RBF approximations, for the first biharmonic equation and its applications in fluid dynamics." International Journal of Numerical Methods for Heat and Fluid Flow. 33 (7), pp. 2593-2616. https://doi.org/10.1108/HFF-11-2022-0673
A new high-order nine-point stencil, based on integrated-RBF approximations, for the first biharmonic equation
Mai-Duy, N., Strunin, D. and Karunasena, W.. 2022. "A new high-order nine-point stencil, based on integrated-RBF approximations, for the first biharmonic equation." Engineering Analysis with Boundary Elements. 143, pp. 687-699. https://doi.org/10.1016/j.enganabound.2022.07.014
Computing high-order derivatives in compact integrated-RBF stencils
Mai-Duy, N., Strunin, D. and Karunasena, W.. 2022. "Computing high-order derivatives in compact integrated-RBF stencils." Engineering Analysis with Boundary Elements. 135, pp. 369-381. https://doi.org/10.1016/j.enganabound.2021.11.025
New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils
Mai-Duy, Nam and Strunin, Dmitry. 2021. "New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils." Engineering Analysis with Boundary Elements. 125, pp. 12-22. https://doi.org/10.1016/j.enganabound.2021.01.001
Parametric Space for Elastic Waves in Porous Media with Complex Rheology
Ali, Adham A. and Strunin, Dmitry V.. 2020. "Parametric Space for Elastic Waves in Porous Media with Complex Rheology." International Journal of Mechanical Engineering and Robotics Research. 9 (6), pp. 825-829. https://doi.org/10.18178/ijmerr.9.6.825-829
Numerical solution of a highly nonlinear and non-integrable equation using integrated radial basis function network method
Bhanot, Rajeev P., Strunin, Dmitry V. and Ngo-Cong, Duc. 2020. "Numerical solution of a highly nonlinear and non-integrable equation using integrated radial basis function network method." Chaos: an interdisciplinary journal of nonlinear science. 30 (8). https://doi.org/10.1063/5.0009215
Rheology and decay rate for Frenkel-Biot P1 waves in porous media with gas bubbles
Strunin, Dmitry V. and Ali, Adham A.. 2019. "Rheology and decay rate for Frenkel-Biot P1 waves in porous media with gas bubbles." International Journal of Mechanics. 13, pp. 156-163.
Rheology and dynamics of elastic waves in fluid-saturated porous media with gas bubbles
Ali, Adham Abdul Wahab. 2019. Rheology and dynamics of elastic waves in fluid-saturated porous media with gas bubbles. PhD Thesis Doctor of Philosophy. University of Southern Queensland. https://doi.org/10.26192/dmgp-0996
Parameters and branching auto-pulses in a fluid channel with active walls
Strunin, Dmitry and Ahmed, Fatima. 2019. "Parameters and branching auto-pulses in a fluid channel with active walls." Fluids. 4 (3). https://doi.org/10.3390/fluids4030160
Nonlinear stability in seismic waves
Ali, Adham A. and Strunin, Dmitry V.. 2017. "Nonlinear stability in seismic waves." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 57, pp. C382-C397. https://doi.org/10.21914/anziamj.v57i0.10441
Dynamics of curved reaction fronts under a single-equation model
Bhanot, R. P. and Strunin, D.V.. 2018. "Dynamics of curved reaction fronts under a single-equation model." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 57, pp. C398-C412. https://doi.org/10.21914/anziamj.v57i0.10446
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. https://doi.org/10.2478/ijame-2018-0031
Simulations of autonomous fluid pulses between active elastic walls using the 1D-IRBFN Method
Ahmed, Fatima Z., Mohammed, Mayada G., Strunin, Dmitry V. and Ngo-Cong, Duc. 2018. "Simulations of autonomous fluid pulses between active elastic walls using the 1D-IRBFN Method ." Mathematical Modelling of Natural Phenomena (MMNP). 13 (5), pp. 1-25. https://doi.org/10.1051/mmnp/2018058
A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils
Ngo-Cong, D., Tien, C.M.T., Nguyen-Ky, T., An-Vo, D.-A., Mai-Duy, N., Strunin, D. V. and Tran-Cong, T.. 2017. "A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils." International Journal for Numerical Methods in Fluids. 85 (7), pp. 404-429. https://doi.org/10.1002/fld.4386
On nonlinear dynamics of neutral modes in elastic waves in granular media
Strunin, D. V. and Ali, A. A.. 2016. "On nonlinear dynamics of neutral modes in elastic waves in granular media." Journal of Coupled Systems and Multiscale Dynamics. 4 (3). https://doi.org/10.1166/jcsmd.2016.1105
Numerical solution for the fluid flow between active elastic walls
Ahmed, F. Z., Strunin, D. V., Mohammed, M. G. and Bhanot, R. P.. 2016. "Numerical solution for the fluid flow between active elastic walls." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 57, pp. C221-C234. https://doi.org/10.21914/anziamj.v57i0.10453
Using 1D-IRBFN method for solving high-order nonlinear differential equations arising in models of active-dissipative systems
Strunin, Dmitry V., Ngo-Cong, Duc and Bhanot, Rajeev. 2015. "Using 1D-IRBFN method for solving high-order nonlinear differential equations arising in models of active-dissipative systems." Idelsohn, Sergio R., Sonzogni, Victorio, Coutinho, Alvaro, Cruchaga, Marcela, Lew, Adrian and Cerrolaza, Miguel (ed.) 1st Pan-American Congress on Computational Mechanics, (PANACM 2015) in conjunction with the XI Argentine Congress on Computational Mechanics (MECOM 2015). Buenos Aires, Argentina 27 - 29 Apr 2015 Barcelona, Spain.
Range of validity and intermittent dynamics of the phase of oscillators with nonlinear self-excitation
Strunin, D. V. and Mohammed, M. G.. 2015. "Range of validity and intermittent dynamics of the phase of oscillators with nonlinear self-excitation." Communications in Nonlinear Science and Numerical Simulation. 29 (1-3), pp. 128-147. https://doi.org/10.1016/j.cnsns.2015.04.024
On dissipative nature of elastic waves
Strunin, D. V.. 2014. "On dissipative nature of elastic waves." Journal of Coupled Systems and Multiscale Dynamics. 2 (2), pp. 70-73. https://doi.org/10.1166/jcsmd.2014.1045
Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution
Ngo-Cong, D., Mohammed, F. J., Strunin, D. V., Skvortsov, A. T., Mai-Duy, N. and Tran-Cong, T.. 2015. "Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution." Journal of Hydrology. 525, pp. 87-101. https://doi.org/10.1016/j.jhydrol.2015.03.038
Soliton-like thermoelastic waves
Strunin, Dmitry and Melnik, Roderick. 2014. "Soliton-like thermoelastic waves ." Hetnarski, Richard B. (ed.) Encyclopedia of thermal stresses. Dordrecht, Netherlands. Springer. pp. 4433-4438
Finite-difference approach for a 6th-order nonlinear phase equation with self-excitation
Mohammed, Mayada and Strunin, Dmitry. 2014. "Finite-difference approach for a 6th-order nonlinear phase equation with self-excitation." Nagamiya, Shoji and Motobayashi, Tohru (ed.) 12th Asia Pacific Physics Conference 2013. Makuhari, Japan 14 - 19 Jul 2013 Makuhari, Japan.
Asymptotics of averaged turbulent transfer in canopy flows
Mohammed, F. J., Strunin, D. V., Ngo-Cong, D. and Tran-Cong, T.. 2015. "Asymptotics of averaged turbulent transfer in canopy flows." Journal of Engineering Mathematics. 91 (1), pp. 81-104. https://doi.org/10.1007/s10665-014-9737-y
Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method
Mohammed, F. J., Ngo-Cong, D., Strunin, D. V., Mai-Duy, N. and Tran-Cong, T.. 2014. "Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 38 (14), pp. 3672-3691. https://doi.org/10.1016/j.apm.2013.12.007
Validity and dynamics in the nonlinearly excited 6th-order phase equation
Strunin, Dimitry and Mohammed, Mayada. 2013. "Validity and dynamics in the nonlinearly excited 6th-order phase equation." Costa, David, Feng, Wei and Feng, Zhaosheng (ed.) 9th American Institute of Mathematical Sciences International Conference on Dynamical Systems, Differential Equations and Applications (AIMS 2013). Orlando, United States 01 - 05 Jul 2012 Springfield, MO. United States.
Numerical analysis of an averaged model of turbulent transport near a roughness layer
Strunin, D. V. and Mohammed, F. J.. 2012. "Numerical analysis of an averaged model of turbulent transport near a roughness layer." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 53 (S), pp. C142-C154.
Parametric space for nonlinearly excited phase equation
Strunin, D. V. and Mohammed, M. G.. 2012. "Parametric space for nonlinearly excited phase equation." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 53 (S), pp. C236-C248.
The role of natural gases in seismics of hydrocarbon reservoirs
Nikolaevskiy, Victor and Strunin, Dmitry. 2012. "The role of natural gases in seismics of hydrocarbon reservoirs." Laverov, N. P., Beresnev, Igor and Gray, Rob (ed.) 3rd International Conference Elastic Wave Effect on Fluid in Porous Media (EWEF 2012). Moscow, Russia 24 - 28 Sep 2012 Moscow, Russia.
Transition to self-similarity of diffusion of tracer in turbulent patch
Strunin, Dmitry V.. 2001. "Transition to self-similarity of diffusion of tracer in turbulent patch." Journal of Engineering Mechanics. 127 (11), pp. 1089-1095. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:11(1089)
Similarity without diffusion: shear turbulent layer damped by buoyancy
Strunin, D. V.. 2006. "Similarity without diffusion: shear turbulent layer damped by buoyancy." Journal of Engineering Mathematics. 54 (3), pp. 211-224. https://doi.org/10.1007/s10665-005-9010-5
On characteristic times in generalized thermoelasticity
Strunin, Dmitry V.. 2001. "On characteristic times in generalized thermoelasticity." Journal of Applied Mechanics. 68 (5), pp. 816-817. https://doi.org/10.1115/1.1386696
Two-zone model of shear dispersion in a channel using centre manifolds
Roberts, A. J. and Strunin, Dmitry V.. 2004. "Two-zone model of shear dispersion in a channel using centre manifolds." The Quarterly Journal of Mechanics and Applied Mathematics. 57 (3), pp. 363-378. https://doi.org/10.1093/qjmam/57.3.363
Modelling the confinement of spilled oil with floating booms
Zhu, Song Ping and Strunin, Dmitry V.. 2001. "Modelling the confinement of spilled oil with floating booms." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 25 (9), pp. 713-729. https://doi.org/10.1016/S0307-904X(01)00008-7
A model of turbulent dispersion through roughness layer using centre manifolds
Strunin, Dmitry V.. 2011. "A model of turbulent dispersion through roughness layer using centre manifolds." Massengill, H. P. (ed.) 6th AIAA Theoretical Fluid Mechanics Conference. Honolulu, United States 27 - 30 Jun 2011 Red Hook, NY. United States.
Universality of turbulent dispersion in a steady flow in an open channel
Strunin, D. V.. 2011. "Universality of turbulent dispersion in a steady flow in an open channel." The Quarterly Journal of Mechanics and Applied Mathematics. 64 (2), pp. 197-214. https://doi.org/10.1093/qjmam/hbr002
Dynamics of two charged particles in viscous fluid at small Reynolds numbers
Stepanyants, Y. A. and Strunin, D. V.. 2011. "Dynamics of two charged particles in viscous fluid at small Reynolds numbers." de Oliveira, Cassiano (ed.) 2011 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Enginnering (MC 2011). Rio de Janeiro, Brazil 08 - 12 May 2011 Rio de Janeiro.
An averaged model of dispersion of pollutant in a channel: logarithmic flow
Strunin, Dmitry V.. 2010. "An averaged model of dispersion of pollutant in a channel: logarithmic flow." Hangos, K. (ed.) 29th IASTED International Conference on Modelling, Identification and Control (MIC 2010). Innsbruck, Austria 15 - 17 Feb 2010 Calgary, Canada.
A new case of truncated phase equation for coupled oscillators
Strunin, Dmitry V.. 2009. "A new case of truncated phase equation for coupled oscillators ." Yahya, Abu Hasan (ed.) 5th Asian Mathematical Conference (AMC2009). Kuala Lumpur, Malaysia 22 - 26 Jun 2009 Kuala-Lumpur, Malaysia.
Modelling turbulent flow from dam break using slow manifolds
Georgiev, D. J., Roberts, A. J. and Strunin, D. V.. 2009. "Modelling turbulent flow from dam break using slow manifolds ." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 50 (S), pp. C1033-C1051.
Effect of canine hyperimmune plasma on TNFa and inflammatory cell levels in a lipopolysaccharide-mediated rat air pouch model of inflammation
Strunin, Dmitry, Essien, Bryan, Kotiw, Michael and Butler, Harry. 2009. "Effect of canine hyperimmune plasma on TNFa and inflammatory cell levels in a lipopolysaccharide-mediated rat air pouch model of inflammation." Reinhart, Konrad (ed.) Sepsis 2009: Critical Care Conference. Amsterdam, Netherlands 11 - 14 Nov 2009 https://doi.org/10.1186/cc8064
Phase equation with nonlinear excitation for nonlocally coupled oscillators
Strunin, D. V.. 2009. "Phase equation with nonlinear excitation for nonlocally coupled oscillators." Physica D: Nonlinear Phenomena. 238 (18), pp. 1909-1916. https://doi.org/10.1016/j.physd.2009.06.022
Low-dimensional boundary-layer model of turbulent dispersion in a channel
Strunin, Dmitry V. and Roberts, Anthony J.. 2009. "Low-dimensional boundary-layer model of turbulent dispersion in a channel." Ao, S. I., Gelman, Len, Hukins, David W. L., Hunter, Andrew and Korsunsky, A. M. (ed.) WCE 2009: World Congress of Engineering . London, United Kingdom 01 - 03 Jul 2009 London, UK.
Fluid flow between active elastic plates
Strunin, D. V.. 2009. "Fluid flow between active elastic plates." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 50 (S), pp. C871-C883.
Two-dimensional particle solution of the extended Hamilton-Jacobi equation
Strunin, D. V.. 2008. "Two-dimensional particle solution of the extended Hamilton-Jacobi equation." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 50 (August), pp. C282-C291.
A mathematical model to account for quantitative iterative effect of TNF-α positive feedback mechanism on inflammatory cascade in TLR-4 mediated TNF-α signaling pathway
Roberts, Tony, Essien, Bryan, Kotiw, Michael, Butler, Harry and Strunin, Dmitry. 2008. "A mathematical model to account for quantitative iterative effect of TNF-α positive feedback mechanism on inflammatory cascade in TLR-4 mediated TNF-α signaling pathway." Ragan, Mark (ed.) 19th International Conference on Genome Informatics (GIW 2008). Gold Coast, Australia 01 - 03 Dec 2008 London, United Kingdom.
Dynamical system approach and attracting manifolds in K-epsilon model of turbulent jet
Strunin, D. V.. 2008. "Dynamical system approach and attracting manifolds in K-epsilon model of turbulent jet." Bulletin of the Belgian Mathematical Society: Simon Stevin. 15 (5), pp. 935-946.
Phenomenological approach to 3D spinning combustion waves: numerical experiments with a rectangular rod
Strunin, Dmitry V. and Suslov, Sergey A.. 2005. "Phenomenological approach to 3D spinning combustion waves: numerical experiments with a rectangular rod." International Journal of Self Propagating High Temperature Synthesis. 14 (1), pp. 33-39.
Universal regimes of a free turbulent jet
Strunin, D. V.. 2007. "Universal regimes of a free turbulent jet." Jacobs, Peter A., McIntyre, Tim, Cleary, Matthew J., Buttsworth, David R., Mee, David, Clements, Rose, Morgan, Richard and Lemckert, Charles (ed.) 16th Australasian Fluid Mechanics Conference (AFMC 2007). Gold Coast, Australia 03 - 07 Dec 2007 Brisbane, Australia.
Attractors in confined source problems for coupled nonlinear diffusion
Strunin, Dmitry V.. 2007. "Attractors in confined source problems for coupled nonlinear diffusion." SIAM Journal on Applied Mathematics. 67 (6), pp. 1654-1674. https://doi.org/10.1137/060657923
A numerical model for the confinement of oil spill with floating booms
Zhu, SongPing and Strunin, Dmitry V.. 2002. "A numerical model for the confinement of oil spill with floating booms." Spill Science and Technology Bulletin. 7 (5-6), pp. 249-255. https://doi.org/10.1016/S1353-2561(02)00042-7
Nonlinear dynamics on centre manifolds describing turbulent floods: k-\omega model
Georgiev, Dian J., Roberts, A. J. and Strunin, Dmitry V.. 2007. "Nonlinear dynamics on centre manifolds describing turbulent floods: k-\omega model." Discrete and Continuous Dynamical Systems Series A.
The dynamics of the vertical structure of turbulence in flood flows
Georgiev, D. J., Roberts, A. J. and Strunin, D. V.. 2007. "The dynamics of the vertical structure of turbulence in flood flows." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 48, pp. C573-C590. https://doi.org/10.0000/anziamj.v48i0.124
Models encompassing hydraulic jumps in radial flows over a horizontal plate
Strunin, Dmitry and Roberts, Tony. 2001. "Models encompassing hydraulic jumps in radial flows over a horizontal plate." Kluev, Vitaly and Mastorakis, Nikos (ed.) 2nd WSEAS Multiconference on Applied and Theoretical Mathematics (WSEAS 2001). Cairns, Australia 17 - 23 Dec 2001 Greece.
Coupled thermomechanical waves in hyperbolic thermoelasticity
Strunin, D. V., Melnik, R. V. N. and Roberts, A. J.. 2001. "Coupled thermomechanical waves in hyperbolic thermoelasticity." Journal of Thermal Stresses. 24 (2), pp. 121-140. https://doi.org/10.1080/01495730150500433
Nonlinear instability in generalized nonlinear phase diffusion equation
Strunin, Dmitry V.. 2003. "Nonlinear instability in generalized nonlinear phase diffusion equation." Progress of Theoretical Physics Supplement.
Attractors and centre manifolds in nonlinear diffusion
Strunin, Dmitry V.. 2005. "Attractors and centre manifolds in nonlinear diffusion." 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asian SIAM Symposium. Hong Kong, China 12 - 16 Dec 2005 Hong Kong.
Nonlinear analysis of rubber-based polymeric materials with thermal relaxation models
Melnik, R. V. N., Strunin, D. V. and Roberts, A. J.. 2005. "Nonlinear analysis of rubber-based polymeric materials with thermal relaxation models." Numerical Heat Transfer Part A: Applications. 47 (6), pp. 549-569. https://doi.org/10.1080/10407780590891236