 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10522 |
| In Russian (ÏÌÌ): | | 9723
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| In English (J. Appl. Math. Mech.): | | 799 |
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| B.D. Annin, N.F. Bel’metsev, and Yu.A. Chirkunov, "A group analysis of the equations of the dynamic transversely isotropic elastic model," J. Appl. Math. Mech. 78 (5), 529-537 (2014) |
| Year |
2014 |
Volume |
78 |
Issue |
5 |
Pages |
529-537 |
| Title |
A group analysis of the equations of the dynamic transversely isotropic elastic model |
| Author(s) |
B.D. Annin (Novosibirsk, Russia, annin@hydro.nsc.ru)
N.F. Bel’metsev (Novosibirsk, Russia, wegsmachine@gmail.com)
Yu.A. Chirkunov (Novosibirsk, Russia, chr101@mail.ru) |
| Abstract |
Group foliation of the system of equations of motion of a transversely isotropic elastic model of geomaterials, satisfying the Gassmann conditions, is carried out. A linear system of first-order differential equations is obtained, equivalent to the equations of this model. A number of theorems describing its properties are proved. A fundamental Lie transformation and an optimum system of its subgroups are obtained, which enable all the invariant, partially invariant and differentially invariant submodels of the dynamic model of a transversely isotropic elastic medium to be obtained. Some exact solutions are derived and their physical meaning is indicated. |
| Received |
16 August 2012 |
| Link to Fulltext |
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