 | | 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
|
| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 48, Issue 2 / 2013 | Next article >> |
| A.O. Vatul'yan and A.A. Lyapin, "On Inverse Coefficient Problems of Poroelasticity," Mech. Solids. 48 (2), 210-215 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
2 |
Pages |
210-215 |
| DOI |
10.3103/S0025654413020131 |
| Title |
On Inverse Coefficient Problems of Poroelasticity |
| Author(s) |
A.O. Vatul'yan (South Federal University, Mil'chakova 8a, Rostov-on-Don, 344090 Russia, vatulyan@math.rsu.ru)
A.A. Lyapin (South Federal University, Mil'chakova 8a, Rostov-on-Don, 344090 Russia, alexlpn@hotmail.com) |
| Abstract |
General approaches to the inverse coefficient problems of poroelasticity on the basis of a modified Biot model are considered. A generalized reciprocity relation is constructed, and an iteration process for determining the unknown coefficients is stated. By way of example, the problem of steady-state longitudinal vibrations of an inhomogeneous poroelastic layered system is considered, and integral equations for the direct and inverse problems are derived. The results of computational experiments where the elastic modulus and the Biot modulus were reconstructed for various laws of variation are given. |
| Keywords |
poroelasticity, vibration, reconstruction of inhomogeneous characteristics |
| References |
| 1. | M. A. Biot,
"Theory of Propagation of Acoustic Waves in a Fluid-Saturated Porous Solid. Part II. Higher Frequency Range,"
J. Acoustic. Soc. Am.
28 (2), 179-191 (1956). |
| 2. | S. C. Cowin and J. W. Nonziano,
"Linear Elastic Materials with Voids,"
J. Elasticity
13 (2), 125-147 (1983). |
| 3. | D. S. Chandrasekharaiah and S. C. Cowin,
"A Complete Solution for a Unified System of Field Equations
of Thermoelasticity and Poroelasticity,"
Acta Mech.
99 (1-4), 225-233 (1993). |
| 4. | J.-F. Allard,
Propagation of Sound in Porous Media: Modeling Sound Absorbing Materials
(Chapman & Hall, London, 1993). |
| 5. | G. Cederbaum, L. P. Li, and K. Schulgasser,
Poroelastic Structures
(Elsevier, Amsterdam, 2000). |
| 6. | S. C. Cowin,
"Bone Poroelasticity,"
J. Biomech.
32 (3), 217-238 (1999). |
| 7. | A. V. Amenitskii, A. A. Belov, L. A. Igumnov, and I. S. Karelin,
"Boundary Integral Equations for Solving Dynamic Problems of Three-Dimensional Theory of Poroelasticity,"
in Problems of Strength and Plasticity, No. 71
(NNGU, Nizhnii Novgorod),
pp. 164-171
[in Russian]. |
| 8. | L. B. Maslov,
Mathematical Modeling of Vibrations of Poroelastic Systems
(PresSto, Ivanovo, 2010)
[in Russian]. |
| 9. | A. O. Vatul'yan,
Inverse Problems in Mechanics of Deformable Solids
(Fizmatlit, Moscow, 2007)
[in Russian]. |
| 10. | A. N. Tikhonov and V. Ya. Arsenin,
Methods for Solving Ill-Posed Problems
(Nauka, Moscow, 1986)
[in Russian]. |
| 11. | A. O. Vatul'yan, O. V. Yavruyan, and I. V. Bogachev,
"Identifying the Elastic Properties of an Inhomogeneously Thick Layer,"
Akust. Zh.
57 (6), 723-730 (2011)
[Acoust. Phys. (Engl. Transl.)
57 (6), 741-748 (2011)]. |
| 12. | A. O. Vatul'yan,
"The Theory of Inverse Problems in the Linear Mechanics of a Deformable Solid,"
Prikl. Mat. Mekh.
74 (6), 909-916 (2010)
[J. Appl. Math. Mech. (Engl. Transl.)
74 (6), 648-653 (2010)]. |
|
| Received |
25 July 2012 |
| Link to Fulltext |
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