 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| T. I. Maslikova and V. S. Polenov, "The propagation of unsteady elastic waves in homogeneous porous media," Mech. Solids. 40 (1), 86-89 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
1 |
Pages |
86-89 |
| Title |
The propagation of unsteady elastic waves in homogeneous porous media |
| Author(s) |
T. I. Maslikova (Voronezh)
V. S. Polenov (Voronezh) |
| Abstract |
A dynamic deformation of a porous medium has been considered in a number
of papers. Among them, we note important papers by M. A. Biot [1-3] in
which the theory of the propagation of steady elastic waves in a
two-component medium has been proposed. The medium was assumed to
consist of an elastic skeleton and pores filled with viscous compressible
fluid. The open pores have a connection with an external surface of the
medium and the isolated pores are elements of the rigid part of the porous
skeleton. The low- and high-amplitude waves have been studied. In [4, 5],
the wave reflection on the free surface of a half-space occupied by a
two-component medium has been considered. The medium was assumed to
consist of elastic and fluid components (wet soil, porous sound-absorbing
materials, pulp).
In this paper, we study unsteady elastic waves in an infinite homogeneous
elastic medium, which are related to one of the topical sections of the
mechanics of structurally nonhomogeneous media. The porosity is regarded
as the local volume discontinuity of the medium, for example, a cavity in
a rigid phase, which is filled with gas as a result of the gas release or
absorbtion during molding. Individual morphological properties of the
pores are determined by their origin. The mechanism of the pore nucleation
in metals is nonhomogeneous. In the general case, the pores can have
arbitrary shape and size. The pores can be localized both inside the metal
and on its boundaries. They can form closed, blind, and through
structures. The degree of porosity is taken into account by the porosity
coefficient m which is equal to the ratio of the total volume of the
pores to the entire volume occupied by the medium. Using the mathematical
discontinuity theory [6] for the basic relations, we show that in the
medium of this kind, two longitudinal waves and one transverse wave can
propagate. Differential equations governing the evolution of the
intensity of the longitudinal and transverse waves during their
propagation are obtained. |
| References |
| 1. | M. A. Biot, "Theory of elasticity and consolidation for a porous
anisotropic solid," Sbornik Perev. Obzorov Inostr. Period. Liter., No. 1,
pp. 140-146, 1956. |
| 2. | M. A. Biot, "Theory of elasticity and consolidation for a porous
anisotropic solid," J. Appl. Phys., Vol. 26, No. 2, pp. 182-185, 1955. |
| 3. | M. A. Biot, "Theory of propagation of elastic waves in a
fluid-saturated porous solid," J. Acoust. Soc. America., Vol. 28, No. 2,
pp. 168-178, 1955. |
| 4. | Ya. I. Frenkel, "On the theory of seismic and seismoelectric
phenomena in a wet soil," Izv. AN SSSR. Ser. Geogr. i Geofiz., Vol. 8,
No. 4, pp. 133-150, 1944. |
| 5. | L. Ya. Kosachevskii, "On the propagation of elastic waves in
two-component media," PMM [Applied Mathematics and Mechanics], Vol. 23, No. 6, pp. 1115-1123, 1959. |
| 6. | T. Thomas, Plastic Flow and Fracture in Solids [Russian
translation], Mir, Moscow, 1964. |
|
| Received |
01 October 2004 |
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