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Abstrakty
Employing Biot’s theory of wave propagation in liquid saturated porous media, waves propagating in a hollow poroelastic circular cylinder of infinite extent are investigated. General frequency equations for propagation of waves are obtained each for a pervious and an impervious surface. Degenerate cases of the general frequency equations of pervious and impervious surfaces, when the longitudinal wavenumber k and angular wavenumber n are zero, are considered. When k=0, the plane-strain vibrations and longitudinal shear vibrations are uncoupled and when […] these are coupled. It is seen that the frequency equation of longitudinal shear vibrations is independent of the nature of the surface. When the angular (or circumferential) wavenumber is zero, i.e., n=0, axially symmetric vibrations and torsional vibrations are uncoupled. For n[…] these vibrations are coupled. The frequency equation of torsional vibrations is independent of the nature of the surface. By ignoring liquid effects, the results of a purely elastic solid are obtained as a special case.
Rocznik
Tom
Strony
565--587
Opis fizyczny
Bibliogr. 19 poz.., tab., wykr.
Twórcy
autor
- Department of Mathematics Deccan College of Engineering and Technology Hyderabad–500 001 (T.S) INDIA
Bibliografia
- [1] Abramowitz A. and Stegun I.A. (1965): Handbook of Mathematical Functions. – National Bureau of Standards, Washington.
- [2] Ahmed Shah S. (2008): Axially symmetric vibrations of fluid-filled poroelastic circular cylindrical shells. – Journal of Sound and Vibration, vol.318, pp.389-405.
- [3] Ahmed Shah S. and Tajuddin M. (2011): Torsional vibrations of poroelastic prolate spheroids. – International Journal of Applied Mechanics and Engineering, vol.16, pp.521-529.
- [4] Berryman J.G. and Pride S.R. (2005): Dispersion of waves in porous cylinders with patchy saturation: Formulation and torsional waves. – J. Acoust. Soc. Am., vol.117, pp.1785-1795.
- [5] Biot M.A. (1956): Theory of propagation of elastic waves in fluid-saturated porous solid. – J. Acoust. Soc. Am., vol.28, pp.168-178.
- [6]Chao G., Smeulders D.M.J. and van Dongen M.E.H. (2004): Shock-induced borehole waves in porous formations: Theory and experiments. – J. Acoust. Soc. Am., vol.116, pp.693-702.
- [7] Farhang H., Esmaeil E., Anthony N.S. and Mirnezami A. (2007): Wave propagation in transversely isotropic cylinders. – Int. Journal of Solids and Structures, vol.44, pp.5236-5246.
- [8] Fatt I. (1959): The Biot-Willis elastic coefficients for a sandstone. – J. Appl. Mech., vol.26, pp.296-297.
- [9] Gazis D.C. (1959): Three-dimensional investigation of the propagation of waves in hollow circular cylinders. – J. Acoust. Soc. Am., vol.31, pp.568-578.
- [10] Karpfinger F., Gurevich B., Valero H.P., Bakulin A. and Sinha B. (2010): Tube wave signatures in cylindrically layered porous media computed with the spectral method. – Geophysical Journal International, vol.183, pp.1005-1013.
- [11] Love A.E.H. (1944): A Treatise on the Mathematical Theory of Elasticity. – New-York: Dover.
- [12] Sharma J.N. and Sharma N. (2010): Three-dimensional free vibration analysis of a homogeneous transradially isotropic thermoelastic sphere. – Trans ASME, J. Appl. Mech., vol.77, 021004 (9 pages).
- [13] Tajuddin M. and Sarma K.S. (1980): Torsional vibrations of poroelastic cylinders. – Trans. ASME, J. Appl. Mech., vol.47, pp.214-216.
- [14] Tajuddin M. and Ahmed Shah S. (2006): Circumferential waves of infinite hollow poroelastic cylinders. – Trans. ASME, J. Appl. Mech., vol.73, pp.705-708.
- [15] Tajuddin M. and Ahmed Shah S. (2007): On torsional vibrations of infinite hollow poroelastic cylinders. – Journal of Mechanics of Materials and Structures, vol.2, pp.189-200.
- [16] Tajuddin M. and Ahmed Shah S. (2010a): Longitudinal shear vibrations of hollow poroelastic cylinders. – Bull. Cal. Math. Soc., vol.102, pp.289-298.
- [17] Tajuddin M. and Ahmed Shah S. (2010b): Radial vibrations of thick-walled hollow poroelastic cylinders. – Journal of Porous Media., vol.13, pp.307-318.
- [18] Wisse C.J., Smeulders D.M.J., van Dongen M.E.H. and Chao G. (2002): Guided wave modes in porous cylinders: Experimental results. – J. Acoust. Soc. Am., vol.112, pp.890-895.
- [19] Yew C.H. and Jogi P.N. (1976): Study of wave motions in fluid-saturated porous rocks. – J. Acoust. Soc. Am., vol.60, pp.2-8.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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