 | | 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
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| In English (Mech. Solids): | | 3212 |
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| I. O. Osipov, "On complex solutions of dynamical problems of plane elasticity for anisotropic bodies in terms of potentials," Mech. Solids. 37 (3), 66-76 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
3 |
Pages |
66-76 |
| Title |
On complex solutions of dynamical problems of plane elasticity for anisotropic bodies in terms of potentials |
| Author(s) |
I. O. Osipov (Petrozavodsk) |
| Abstract |
In [1], the method of complex solutions suggested by V. I. Smirnov and
S. L. Sobolev [2-4] is applied (in terms of potentials) to dynamical
problems of plane elasticity for anisotropic media with three elastic
parameters satisfying the constraint (a−d)a−c2>0. Due to a
methodological inconsistency committed in [1], the solutions obtained are
in disagreement with the physical meaning of the problem and similar
solutions for isotropic media. In the present paper, the investigation of
this problem is continued by the same method for anisotropic bodies with
four elastic constants and no additional constraints on these constants. A
new approach is proposed for the construction of solutions of the equations
of motion. We obtain and investigate solutions describing plane waves and
waves arising from a point source such as an instantaneous impulse, as well
as complex solutions of general type. The solutions
obtained here differ from those of [1] and are in agreement with the
physical meaning of the problem and similar solutions for anisotropic
media. |
| References |
| 1. | V. A. Sveklo, "On the solution of dynamical problems of plane
elasticity for anisotropic bodies," PMM [Applied Mathematics and
Mechanics], Vol. 25, No. 5, pp. 885-896, 1961. |
| 2. | V. I. Smirnov and S. L. Sobolev,
"A new method for solving the plane problem of elastic vibrations,"
in Trudy Seismolog. In-ta AN SSSR [in Russian], No. 20, 1932. |
| 3. | S. L. Sobolev, "Some issues of the theory of propagation of
vibrations," in F. Frank and R. Mises. Differential Equations of
Mathematical Physics [Russian translation], pp. 468-617, ONTI, Moscow, Leningrad, 1937. |
| 4. | V. I. Smirnov, A Course in Higher Mathematics [in Russian], Gostekhizdat,
Moscow, 1953. |
| 5. | V. A. Sveklo, "Elastic vibrations of anisotropic bodies,"
Uchen. Zapiski LGU, Ser. Mat., No. 17, pp. 28-71, 1949. |
| 6. | I. O. Osipov, "On the plane problem of elastic
vibrations caused by a point source in anisotropic media,"
PMM [Applied Mathematics and Mechanics], Vol. 33, No. 3, pp. 548-555, 1969. |
| 7. | I. O. Osipov, "Propagation of plane waves in an elastic medium
in contact with a fluid," Izv. AN SSSR. MTT [Mechanics of Solids],
No. 6, pp. 144-154, 1989. |
| 8. | I. O. Osipov, "On wave processes and sharp edges of wave fronts
in anisotropic media with a point source of waves," PMM
[Applied Mathematics and Mechanics], Vol. 36, No. 5, pp. 927-934, 1972. |
| 9. | I. O. Osipov, "On the character of variation of elastic wave
propagation velocities in anisotropic media," Izv. AN SSSR. Ser. Geofiz.,
No. 1, pp. 3-10, 1962. |
| 10. | I. O. Osipov, "On the method of complex solutions of dynamical
problems of plane elasticity for anisotropic bodies," Izv. AN. MTT
[Mechanics of Solids], No. 4, pp. 102-112, 1999. |
| 11. | G. I. Petrashen', Wave Propagation in Anisotropic Elastic Media
[in Russian], Nauka, Leningrad, 1980. |
| 12. | N. V. Zvolinskii, M. I. Reitman, and G. S. Shapiro,
"Dynamics of solids,"in 50 Years of Mechanics in the USSR. Volume 3
[in Russian], pp. 291-323, Nauka, Moscow, 1972. |
| 13. | V. D. Kupradze, Methods of Potential in Elasticity [in Russian],
Fizmatgiz, Moscow, 1963. |
| 14. | V. D. Kupradze, T. G. Gegelia, M. O. Basheleishvili, and
T. V. Burchuladze, Three-Dimensional Problems of Mathematical Elasticity
[in Russian], Izd-vo Tbilissk. Un-ta, Tbilisi, 1968. |
|
| Received |
26 April 2000 |
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