Analytical Solutions for Harmonic Wave Propagation in Poroelastic Media
Publication: Journal of Engineering Mechanics
Volume 120, Issue 10
Abstract
This paper presents several analytical solutions for problems of harmonic wave propagation in a poroelastic medium. The pressure‐solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. Then these equations are solved for several particular situations. Closed‐form analytical solutions are obtained for several basic problems: independent plane harmonic waves; radiation from a harmonically oscillating plane wall; radiation from a pulsating sphere; and the interior eigenvalue problem for a sphere, for the cases of both a rigid surface and a traction‐free surface. Finally, a series solution is obtained for the case of a plane wave impinging on a spherical inhomogeneity. This inhomogeneity is composed of poroelastic material having different properties from those of the infinite poroelastic medium in which it is embedded, and the incident wave may be composed of any linear combination of Biot “fast” and “slow” waves.
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References
1.
Berryman, J. G. (1985). “Scattering by a spherical inhomogeneity in a fluid‐saturated porous medium.” J. Math. Phys., 26(6), 1408.
2.
Biot, M. A. (1956). “Theory of propagation of elastic waves in a fluid‐saturated porous solid.” J. Acoust. Soc. Am., Vol. 28, 168.
3.
Biot, M. A. (1962). “Mechanics of deformation and acoustic propagation in porous media.” J. Appl. Phys., Vol. 33, 1482.
4.
Biot, M. A., and Willis, D. C. (1957). “The elastic coefficients of the theory of consolidation.” J. Appl. Mech., Vol. 24, 594.
5.
Bonnet, G. (1987). “Basic singular solutions for a poroelastic medium in the dynamic range.” J. Acoust. Soc. Am., 82(5), 1758.
6.
Deresiewicz, H., and Rice, J. T. (1962). “The effect of boundaries on wave propagation in a liquid filled porous solid.” Bull. Seismol. Soc. Am., Vol. 52, 595.
7.
Hamilton, E. L. (1976). “Sound attenuation as a function of depth in the seafloor.” J. Acoust. Soc. Am., Vol. 59, 528.
8.
Kargl, S., and Lim, R. (1993). “A transition matrix formalism for scattering in homogeneous, saturated, porous media.” J. Acoustical Soc. Am., 94(3), 1527.
9.
Morse, P. M., and Feshbach, H. (1953). Methods of theoretical physics. McGraw‐Hill, New York, N.Y.
10.
Norris, A. N. (1985). “Radiation from a point source and scattering theory in a fluid‐saturated porous medium.” J. Acoust. Soc. Am., Vol. 77, 2012.
11.
Norris, A. N. (1989). “Stoneley‐wave attenuation and dispersion in permeable formations.” Geophys., 54(3), 330.
12.
Pao, Y. H., and Mow, C. C. (1963). “Scattering of plane compressional waves by a spherical obstacle.” J. Appl. Physics, 34(3), 493.
13.
Stern, M., Bedford, A., and Millwater, H. R. (1985). “Wave reflection from a sediment layer with depth‐dependent properties.” J. Acoust. Soc. Am., 77(5), 1781.
14.
Stoll, R. D., and Bryan, G. M. (1970). “Wave attenuation in saturated sediments.” J. Acoust. Soc. Am., 47(5), 1440.
15.
Stoll, R. D. (1980). “Theoretical aspects of sound transmission in sediments.” J. Acoust. Soc. Am., 68(5), 1341.
16.
Stoll, R. D., and Kan, T. K. (1982). “Reflection of acoustic waves at a water‐sediment interface.” J. Acoust. Soc. Am., Vol. 72, 556.
17.
Zimmerman, C., and Stern, M. (1993). “Scattering of plane compressional waves by spherical inclusions in a poroelastic medium.” J. Acoust. Soc. Am., 94(1), 527.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 120 • Issue 10 • October 1994
Pages: 2154 - 2178
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Mar 18, 1993
Published online: Oct 1, 1994
Published in print: Oct 1994
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