 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
|
| << Previous article | Volume 46, Issue 5 / 2011 | Next article >> |
| A.V. Shekoyan, "Waves in a Solid Medium with Liquid-Filled Pores," Mech. Solids. 46 (5), 788-797 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
5 |
Pages |
788-797 |
| DOI |
10.3103/S002565441105013X |
| Title |
Waves in a Solid Medium with Liquid-Filled Pores |
| Author(s) |
A.V. Shekoyan (Institute of Mechanics, National Academy of Sciences of Republic of Armenia, Marshal Baghramian ave., 24B, Erevan, 375019 Republic of Armenia, ashotshek@mechins.sci.am) |
| Abstract |
The dynamic nonlinear theory of deformation of a two-phase medium, a solid with pores filled with a liquid, is developed. The variational principle is used to derive nonlinear equations that take into account the motions of the solid and liquid phases and the porosity variations. All types of nonlinearity, including nonlinear friction, are also taken into account. Formulas for the velocities of the linear and nonlinear waves and the absorption coefficient are derived. The one- and three-dimensional cases are considered. In the three-dimensional case, an equation describing the wave profile evolution is obtained as well as a nonlinear Schrödinger equation. Their solutions are analyzed; soliton-type solutions and solutions for narrow beams are obtained. |
| Keywords |
wave, two-phase medium, nonlinearity, solid body, liquid, evolution equation, modulation equation |
| References |
| 1. | M. A. Biot,
"General Theory of Three-Dimensional Consolidation,"
J. Appl. Phys.
12, 155-164 (1941). |
| 2. | Ya. I. Frenkel,
"On the Theory of Seismic and Seismoelectric Phenomena in a Moist Soil,"
Izv. Akad. Nauk SSSR. Ser. Geogr. Geofiz.
8 (4), 133-149 (1944). |
| 3. | M. A. Biot,
"Mechanics of Deformation and Acoustic Propagation in Porous Media,"
J. Appl. Phys.
33 (4), 1482-1498 (1962). |
| 4. | V. A. Florin,
Theory of Consolidation of Ground Masses
(Stroiizdat, Moscow, 1948)
[in Russian]. |
| 5. | G. I. Barenblatt,
"On Some Approximate Methods in the Theory of One-Dimensional Unsteady Filtration
of Liquid under Elastic Operation Mode,"
Izv. Akad. Nauk SSSR. OTN. Mekh. Mashinostr.,
No. 9, 35-49 (1954). |
| 6. | L. Ya. Kosachevskii,
"On the Propagation of Elastic Waves in Two-Phase Media,"
Prikl. Mat. Mekh.
23 (6), 1115-1123 (1959)
[J. Appl. Math. Mech. (Engl. Transl.)
23 (6), 1593-1604 (1959)]. |
| 7. | M. A. Biot,
"General Theory of Acoustic Propagation in Porous Dissipative Media,"
J. Acoust. Soc. Amer.
34, Pt. 1, 1254-1264 (1962). |
| 8. | V. N. Nikolaevskii, K. S. Basniev, A. T. Gorbunov, and G. A. Zotov,
Mechanics of Saturated Porous Media
(Nedra, Moscow, 1970)
[in Russian]. |
| 9. | R. I. Nigmatulin,
Foundations of Mechanics of Heterogeneous Media
(Nauka, Moscow, 1978)
[in Russian]. |
| 10. | V. N. Nikolaevskii,
Geomechanics and Fluid Dynamics.
With Applications to Problems of Gas and Oil Strata
(Nedra, Moscow, 1996)
[in Russian]. |
| 11. | V. G. Bykov,
Seismic Waves in Porous Saturated Rocks
(Dalnauka, Vladivostok, 1999)
[in Russian]. |
| 12. | N. S. Gorodetskaya,
"Wave Attenuation at Symmetric Vibrations of a Porous-Elastic
Layer with Free Surfaces,"
Akust. Vestnik
1 (4), 4-18 (1998). |
| 13. | S. E. Dasso,
"Quantifying Uncertainty in Geoacoustic Inversion,"
J. Acoust. Soc. Amer.
111, Pt. 1 (1), 129-142 (2002). |
| 14. | R. D. Stall,
"Velocity Dispersion in Water-Saturated Granular Sediment,"
J. Acoust. Soc. Amer. 111 (2), 785-793 (2002). |
| 15. | V. V. Gushchin and G. M. Shalashov,
"Possibility of Using Nonlinear Seismic Effects in Problems
of Vibration Transluscence of the Earth,"
in Study of the Earth with Nonexplosive Seismic Sources
(Nauka, Moscow, 1981), pp. 144-155
[in Russian]. |
| 16. | S. L. Lopatnikov and A. H.-D. Cheng,
"Macroscopic Lagrangian Formulation of Poroelasticity with Porosity Dynamics,"
Mech. Phys. Solids
52 (12), 2801-2839 (2004). |
| 17. | M. G. Markov,
"Effect of Interfacial Slip on the Kinematic and Dynamic Parameters
of Elastic Waves in a Fluid-Saturated Porous Medium,"
Akust. Zh.
53 (2), 249-253 (2007)
[Acoust. Phys. (Engl. Transl.)
53 (2), 213-216 (2007)]. |
| 18. | L. A. Molotkov,
Study of Wave Propagation in Porous and Cracked Media
on the Basis of Effective Biot Models in Layered Media
(Nauka, St. Petersburg, 2001)
[in Russian]. |
| 19. | T. W. Wright,
"Elastic Wave Propagation through a Material with Voids,"
J. Mech. Phys. Solids
46 (10), 2033-2047 (1998). |
| 20. | R. Kumar and S. Choundhary,
"Disturbance due to Mechanical Sources in Micropolar Elastic Medium with Voids,"
J. Sound Vibr.
256 (1), 1-15 (2002). |
| 21. | A. V. Nikolaev and I. N. Galkin (Editors),
Problems of Nonlinear Seismicity
(Nauka, Moscow, 1987)
[in Russian]. |
| 22. | A. S. Aleshin, V. V. Gushchin, M. M. Krekov, A. V. Nikolaev, A. V. Sokolov, and G. N. Shalashov,
"Experimental Studies of Nonlinear Seismic Surface Waves,"
Dokl. Akad. Nauk SSSR
260 (3), 574-575 (1981). |
| 23. | V. G. Bykov,
Nonlinear Wave Processes in Geological Media
(Dal'nauka, Vladivostok, 2000)
[in Russian]. |
| 24. | A. M. Ionov, V. K. Sirotkin, and E. V. Sulin,
"Propagation of Nonlinear Longitudinal Waves in Porous Saturated Media,"
Zh. Prikl. Mekh. Tekhn. Fiz.,
21 (6), 138-144 (1988)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
21 (6), 894-899 (1988)]. |
| 25. | V. G. Bykov and V. N. Nikolaevskii,
"Nonlinear Geoacoustic Waves in Marine Sediments,"
Akust. Zh.
36 (4), 606-610 (1990)
[Sov. Phys. Acoust. (Engl. Transl.)
36 (4), 342-344 (1990)]. |
| 26. | A. G. Bagdoev and A. V. Shekoyan,
"Nonlinear Waves in a Two-Component Viscous Medium with Voids,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 91-100 (2004)
[Mech. Solids (Engl. Transl.)
39 (3), 73-80 (2004)]. |
| 27. | L. I. Sedov,
Continuum Mechanics, Vol. 1
(Nauka, Moscow, 1994)
[in Russian]. |
| 28. | V. L. Berdichevskii,
Variational Principles of Continuum Mechanics
(Nauka, Moscow, 1983)
[in Russian]. |
| 29. | L. D. Landau and E. M. Lifshitz,
Course of Theoretical Physics, Vol. 2: The Classical Theory of Fields
(Nauka, Moscow, 1967; Butterworth-Heinemann, 1980). |
| 30. | L. K. Zarembo and V. A. Krasilnikov,
Introduction to Nonlinear Acoustics
(Nauka, Moscow, 1966)
[in Russian]. |
| 31. | A. G. Bagdoev and A. V. Shekoyan,
"Nonlinear Waves in a Solid Viscous Medium with Cavities,"
Akust. Zh.
45 (2), 149-156 (1999)
[Acoust. Phys. (Engl. Transl.)
45 (2), 119-126 (1999)]. |
| 32. | N. A. Kudryashov,
"Bäcklund Transformation for a Fourth-Order Partial Differential Equation
with the Burgers-Korteweg-de Vries Nonlinearity,"
Dokl. Akad. Nauk SSSR
300 (2), 342-344 (1988)
[Sov. Phys. Dokl. (Engl. Transl.)
33, 336-338 (1988)]. |
| 33. | A. G. Bagdoev, G. Oganyan, and A. V. Shekoyan,
"On Some Analytical Solutions of Evolution Equation with Nonstandard Nonlinearity
for Current-Conducting Fluid-Saturated Soils,"
Izv. NAN RA. Mekh.
56 (3), 49-54 (2003). |
| 34. | S. A. Akhmanov, A. P. Sukhorukov, and R. V. Khokhlov,
"Self-Focusing and Diffraction of Light in a Nonlinear Medium,"
Uspekhi Fiz. Nauk
93 (1), 19-70 (1967)
[Sov. Phys. Uspekhi (Engl. Transl.)
10 (5), 609-636 (1968)]. |
| 35. | A. G. Bagdoev and A. V. Shekoyan,
"Three-Dimensional Nonlinear Waves in Piezodielectrics and
Piezosemiconductors,"
Izv. Akad. Armyan. SSR. Ser. Mat.
34 (4), 3-15 (1981)
[Sov. J. Contemp. Math. Anal., Arm. Acad. Sci. (Engl. Transl.)]. |
| 36. | M. B. Vinogradov, O. V. Sukhorukov, and A. P. Rudenko,
Theory of Waves
(Nauka, Moscow, 1979)
[in Russian]. |
|
| Received |
31 March 2009 |
| Link to Fulltext |
|
| << Previous article | Volume 46, Issue 5 / 2011 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English