Symmetric wave propagation in a non-homogeneous fluid saturated incompressible porous medium

• Autorzy: Kumar R. , Hundal B. S.
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to study the propagation of cylindrical and spherical waves in a fluid saturated nonhomogeneous incompressible porous medium. The governing equations are solved by the method of characteristics. Characteristic equations and the relations for the discontinuities across the wave fronts are derived. Two particular models with different non-homogeneity functions and for different loads are taken for numerical investigation.

Słowa kluczowe

EN

Fillunger model; incompressible porous medium; volume fractions; symmetric waves; characteristic equations; discontinuity relations; characteristic

PL

tworzywa nieściśliwe; tworzywa porowate; tarcie; tarcie powierzchniowe

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2008
• Tom: Vol. 13, no 1
• Strony: 155--174
• Opis fizyczny: Bibliogr. 46 poz., wykr.

Twórcy

autor

Kumar R.

autor

Hundal B. S.

• Department of Mathematics Kurukeshtra University, Kurukeshtra Haryana, INDIA,

Bibliografia

• Achenbach J.D. (1973): Wave Propagation in Elastic Solids. - North-Holland, Amesterdam.
• Ames W.F. (1977): Numerical Methods for Partial Differential Equations. - Academic Press, New York.
• Biot M.A. (1941): General theory of three dimensional consolidation. - J. Appl. Phys., vol.12, pp.155-164.
• Biot M.A. (1956a): Theory of propagation of elastic waves in a fluid-saturated porous solid - I. Low frequency range. - J. Acout. Soc. Am., vol.28, pp.168-178.
• Biot M.A. (1956b): Theory of propagation of elastic waves in a fluid-saturated porous solid - II. Higher frequency range. - J. Acout. Soc. Am., vol.28, pp.179-191.
• Bowen R.M. (1980): Incompressible porous media models by use of the theory of mixtures. - Int. J. Eng. Sci., vol.18, pp.1129-1148.
• Chou P.C. and Koenig H.A. (1966): A unified approach to cylindrical and spherical elastic waves by method of characteristics. - J. Appl. Mech., vol.33, pp.159-167.
• Chou P.C. and Mortimer R.W. (1967): Solution of one-dimensional elastic wave problems by the method of characteristics. - J. Appl. Mech., vol.41, pp.745-750.
• Chou P.C. and Gordon P.F. (1967): Radial propagation of axial shear waves in a non-homogeneous elastic media. - J. Acoust. Soc. Am., vol.42, pp.36-41.
• Clifton R.J. (1967): On a difference method for plane problems in dynamic elasticity. - Q. Appl. Math., vol.25, pp.97-116.
• Courant R. and Hilbert D. (1975): Methods of Mathematical Physics. - Vol.2. Wiley Eastern Private Limited, New Delhi.
• de Boer R. and Ehlers W. (1988): A historical review of the formulation of porous media theories. - Acta Mechanica, vol.74, pp.1-8.
• de Boer R. (1996): Highlights in the historical development of the porous media theory: Toward a consistent macroscopic theory. - Appl. Mech. Rev., vol.49, pp.201-262.
• de Boer R.. (2000a): Theory of Porous Media. - Springer-Verlag New York.
• de Boer R.. (2000b): Contemporary progress in porous media theory. - Appl. Mech. Rev., vol.53, pp.323-370.
• de Boer R. and Ehlers W. (1990): The development of the concept of effective stress. - Acta Mechanica, vol.83, pp.77-92.
• de Boer R. and Ehlers W. (1990): Uplift, friction and capillarity - three fundamental effects for liquid-saturated porous solids. - Int. J. Solid Structures, vol.26, pp.43-57.
• de Boer R., Ehlers W. and Liu Z. (1993): One-dimensional transient wave propagation in a fluid-saturated incompressible porous media. - Arch. App. Mech., vol.63, pp.59-72.
• de Boer R. and Liu Z. (1996): Growth and decay of acceleration waves in incompressible saturated poroelastic solids. - TIPM, vol.76, pp.341-347.
• Ehlers W. (1993): Compressible, incompressible and hybrid two-phase models in porous theories. - ASME; AMD, vol.158, pp.25-38.
• Fillunger P. (1933): Der Auftrieb in Talsperren. Osterr. Wochenschrift fur den offentl. Baudienst. - I. Teil 532-552, II. Teil 552-556, III. Teil 567-570.
• Garabedian P.R. (1964): Partial Differential Equations. - John Wiley, New York.
• Holt M. (1984): Numerical Methods in Fluid Dynamics. - 2nd ed., Springer-Verlag, New York.
• Hopkins H.G. (1960): Dynamic expansion of spherical cavities in metal. - Progress in Solid Mechanics, vol.1, North Holand Publishing Company, Amstredam, Holand, pp.84-164.
• Jefferey A. and Taniuty T. (1964): Non-linear Wave Propagation. - Academic Press, New York.
• Kevorkian J. (1990): Partial Differential Equations, Analytical Solution Techniques. - Wadsworth and Brooks, Pacific City, CA.
• Knobel R. (2000): An Introduction to the Mathematical Theory of Waves. - American Mathematical Society, Providence, Rhode Island.
• Kumar R. and Hundal B.S. (2003): Wave propagation in a fluid-saturated incompressible porous medium. - Indian J. Pure and Applied Math., vol.4, pp.651-65.
• Kumar R. and Hundal B.S. (2005): Symmetric wave propagation in a fluid-saturated incompressible porous medium. - J. Sound and Vibration, vol.288, pp.361-373.
• Lekan O. (1986): Vibration analysis of spherical shells. - Int. J. Eng. Sci., vol.24, pp.1637-1654.
• Liu Z. and de Boer R. (1994): Plane waves in a semi-infinite fluid saturated porous medium. - TIPM, vol.16, pp.147-173.
• Liu Z. and de Boer R. (1995): Propagation of acceleration waves in incompressible saturated porous solids. - TIPM, vol.21, pp.163-173.
• Liu Z. and de Boer R. (1997): Dispersion and attenuation of surface waves in a fluid-saturated porous medium. - TIPM, vol.29, pp.207-223.
• Liu Z. (1999): Propagation and evolution of wave fronts in two-phase porous media. - TIPM, pp.34, pp.209-225.
• Shim V.P.W. and Quah S.E. (1998): Solution of impact induced flexural waves in a circular ring by the method of characteristics. - J. Appl. Mech., vol.65, pp.569-579.
• Sneddon I.N. (1957): Elements of Partial Differential Equations. - McGraw-Hill Book Company, Inc. New York.
• Sumi N. (2001): Numerical solutions of thermoelastic wave problems by the method of characteristics. - J. Thermal Stress, vol.24, pp.509-530.
• Sumi N. and Ashida F. (2003): Solution for thermal and mechanical waves in a piezoelectric plate by the method of characteristics. - J. Thermal Stress, vol.26, pp.1113-1123.
• Svanadze M. and de Boer R. (2005): On the representation of solutions in the theory of fluid-saturated incompressible porous media. - Q. J. Mech. Appl. Math, vol.58, No.4, pp.551-562.
• Tran D.V.D. and Singh M.C. (2004): Nonlinear uniaxial thermoelastic waves by the method of characteristics. - J. Thermal Stress, vol.27, pp.741-777.
• Zucrow M.J. and Hoffman J.D. (1976): Gas Dynamics. - Wiley, New York.
• Ziv M. (1969): Two-spatial dimensional elastic wave propagation by the theory of characteristics. - Int. J. Solids Struct., vol.5, pp.1135-1151.
• Ziv M. (1975): A general solution method for transient multi-dimensional problems in solid mechanics. - Bull. Seismol. Soc. Am., vol.65, No.5, pp.1359-1384.
• von Terzaghi K. (1923): Die Berechnug der Durchlassigkeit des Tones aus dem Verlauf der hydromechanischen Spannungserscheinungen. - Sitzungsber. Akad. Wiss. (Wien), Math. - Naturwiss. Kl., Abt. IIa 132, pp.125-138.
• von Terzaghi K. (1925): Erdbaumechanik auf Bodenphysikalischer Grundlage. - p.399. Leipzig - Wien: Franz Deuticke.
• Yan Bo, Liu Z. and Zhang X. (1999): Finite element analysis of wave propagation in a fluid-saturated porous media. - Applied Mathematics and Mechanics, vol.20, pp.1331-1341.