Skip to main content
SpringerLink
Log in

Fundamental and plane wave solution in swelling porous medium

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

In the present paper propagation of plane waves in swelling porous medium (SP) is studied. The phase velocity and attenuation coefficients of these waves are computed numerically and presented graphically. The results so obtained have been compared to without swelling porous elastic medium (EL). The fundamental solution of the system of differential equations in swelling porous medium in case of steady oscillations in terms of elementary functions has been constructed. Some basic properties are established and particular case of interest is also deduced.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Atkin, R.J., Craine, R.E.: Continuum theories of mixtures: basic theory and historical development. Q. J. Mech. Appl. Math. 29, 209–245 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  2. Atkin, R.J., Craine, R.E.: Continuum theories of mixtures: applications. J. Int. Math. Appl. 17, 153–207 (1976)

    MATH  MathSciNet  Google Scholar 

  3. Bedford, A., Drumheller, D.S.: Theory of immiscible and structured mixtures. Int. J. Eng. Sci. 21, 863–960 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  4. Eringen, A.C.: A Continuum theory of swelling porous elastic soils. Int. J. Eng. Sci. 32, 1337–1349 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bofill, F., Quintanilla, R.: Anti plane shear deformations of swelling porous elastic soils. Int. J. Eng. Sci. 41, 801–816 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gales, C.: Waves and vibrations in the theory of swelling porous elastic soils. Eur. J. Mech. A Solids 23, 345–357 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Tessa, W., Bennethum, S.: On the derivation of the transport equation for swelling porous materials with finite deformation. Int. J. Eng. Sci. 44, 1408–1422 (2006)

    Article  MATH  Google Scholar 

  8. Kleinfelter, N., Park, M., Cushman, J.: Mixture theory and unsaturated flow in swelling soils. Transp. Porous Med. 68, 69–89 (2007)

    Article  MathSciNet  Google Scholar 

  9. Gales, C.: On the asymptotic spatial behavior in the theory of mixtures of thermo elastic solids. Int. J. Solids Struct. 45, 2117–2127 (2008)

    Article  MATH  Google Scholar 

  10. Gales, C.: On spatial behavior of the harmonic vibrations in thermoviscoelastic mixtures. J. Thermal Stresses 32, 512–529 (2009)

    Article  Google Scholar 

  11. Zhu, H., Dhall, A., Mukherjee, S., Datta, A.: A model for flow and deformation in unsaturated swelling porous media. Transp. Porous Med. 84, 335–369 (2010)

    Article  MathSciNet  Google Scholar 

  12. Jahanshahi, E., Gandjalikhan, A., Jafari, S.: Numerical simulation of a three layered radiant porous heat exchanger including lattice Boltzmann simulation of fluid flow. Int. J. Eng. 24(3), 301–319 (2011)

    Google Scholar 

  13. Shahanzari, R., Ziabasharhagh, M., Talsaz, H.: Comparison of thermal dispersion effects for single and two phase analysis of heat transger in porous media. Int. J. Eng. 24(1), 81–91 (2011)

    Google Scholar 

  14. Merlani, A., Salusti, E., Violini, G.: Non-linear waves fluid pressure and contaminant density in swelling shales. J. Petroleum Sci. and Engng. 79, 1–9 (2011)

    Article  Google Scholar 

  15. Heider, Y., Markert, B., Ehlers, W.: Dynamic wave propagation in infinite saturated porous media half spaces. Comput Mech. 49, 319–336 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  16. Svanadze, M.: Fundamental solution of the system of equations of steady oscillations in the theory of microstretch elastic solids. Int. J. Eng. Sci. 42, 1897–1910 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Boer, R., Svanadze, M.: Fundamental solution of the system of equations of steady oscillations in the theory of fluid-saturated porous media. Transp. Porous Media 56, 39–50 (2004)

    Article  MathSciNet  Google Scholar 

  18. Svanadze, M., Cicco, S.: Fundamental solution in the theory of thermomicrostretch elastic solids. Int. J. Eng. Sci. 43, 417–431 (2005)

    Article  MATH  Google Scholar 

  19. Ciarletta, M., Scalia, A., Svanadze, M.: Fundamental solution in the theory of micropolar thermoelasticity for materials with voids. J Thermal Stress 30, 213–229 (2007)

    Article  MathSciNet  Google Scholar 

  20. Svanadze, M., Giordano, P., Tibullo, V.: Basic properties of the fundamental solution in the theory of micropolar thermoelasticity without energy dissipation. J. Thermal Stresses 33, 721–753 (2010)

    Article  Google Scholar 

  21. Hormander, L.: Linear Partial Differential Operators. Springer, Berlin (1976)

    Google Scholar 

  22. Kupradze, V.D., Gegelia, T.G., Bashekeishvili, M.O., Burchuladze, T.V.: Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. North-Holland, Amsterdam (1979)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana,  136 119, India

    Rajneesh Kumar

  2. Department of Mathematics, N.I.T., Kurukshetra, Haryana,  136 119, India

    Divya Taneja & Kuldeep Kumar

Authors
  1. Rajneesh Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Divya Taneja
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kuldeep Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Divya Taneja.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kumar, R., Taneja, D. & Kumar, K. Fundamental and plane wave solution in swelling porous medium. Afr. Mat. 25, 397–410 (2014). https://doi.org/10.1007/s13370-012-0123-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-012-0123-5

Keywords

Mathematics Subject Classification (2000)

Search

Navigation