 | | 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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| M.Sh. Israilov, "Coupled Seismic Vibrations of a Pipeline in an Infinite Elastic Medium," Mech. Solids. 51 (1), 46-53 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
1 |
Pages |
46-53 |
| DOI |
10.3103/S0025654416010052 |
| Title |
Coupled Seismic Vibrations of a Pipeline in an Infinite Elastic Medium |
| Author(s) |
M.Sh. Israilov (Research Institute of Mathematical Physics and Seismodynamics, Chechen State University, ul. Kievskaya 33, Groznyy, 364037 Russia, israiler@hotmail.com) |
| Abstract |
The exact solution of the problem of coupled seismic vibrations of an underground pipeline and an infinite elastic medium is given. A method dramatically simplifying the solution of the exterior problem for the medium is proposed on the basis of the established theorem on the separation of the boundary conditions for the wave potentials on the surface of the cylinder. The obtained results permit improving the incorrect consideration of the problem accepted in the literature.
The exact statement of the problem allows one to use the solution of the problem as a test for estimating the accuracy of appropriate approaches and solutions in seismodynamics of extended underground structures.
The results of comparison show that the solutions practically coincide both in the subsonic operation mode (when the seismic wave velocity is smaller than the rod velocity of wave propagation in the pipeline) and in the supersonic operation mode, where a resonance is possible. Thus, the high accuracy of the significantly simpler theory of one-dimensional deformation is confirmed. |
| Keywords |
seismodynamics, underground pipeline, seismic vibrations, elastic waves |
| References |
| 1. | N. M. Newmark,
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in Proc. of the Intern. Symposium on Wave Propagation
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(Univ. of New Mexico Press, 1968),
pp. 7-26. |
| 2. | A. Sakurai and T. Takahashi,
"Dynamic Stress of Underground Pipelines during Earthquakes,"
in Proc. of the 4th World Conf. on Earth. Engng (4WCEE), Santiago, Chile, Vol. 2
(1969),
pp. 811-895. |
| 3. | A. A. Il'yushin and T. R. Rashidov,
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(2012),
p. 2125. |
| 5. | M. Sh. Israilov,
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Probl. Mekh. Akad. Nauk RUz,
No. 3, 18-24 (2012). |
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24(2) (221), 107-125 (1974). |
| 7. | M. Sh. Israilov,
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No. 1, 131-136 (2011)
[Mech. Solids (Engl. Transl.)
46 (1), 104-108 (2011)]. |
| 8. | V. D. Kupradze,
Dynamic Problems in Elasticity,
in Progress in Solid Mechanics, Vol. 3,
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(North-Holland, Amsterdam, 1963). |
| 9. | M. Sh. Israilov,
Dynamic Theory of Elasticity and Wave Diffraction
(Izdat. MGU, Moscow, 1992)
[in Russian]. |
| 10. | N. N. Lebedev,
Special Functions and Their Applications
(Fizmatlit, Moscow-Leningrad, 1963)
[in Russian]. |
| 11. | T. Rashidov,
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Dokl. Akad. Nauk UzSSR,
No. 9, 10-12 (1962). |
| 12. | M. A. Biot,
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No. 3 (19), 142-155 (1953). |
| 13. | M. Ewing, W. S. Jardetzky, and F. Press,
Elastic Waves in Layered Media
(McGraw-Hill, New York, 1957). |
| 14. | J. E. White,
"Elastic Waves along Cylindrical Bore,"
Geophys.
27 (3), 327-333 (1962). |
| 15. | J. E. White,
Seismic Waves. Radiation, Transmission, and Attenuation
(McGraw-Hill, New York, 1965). |
|
| Received |
12 March 2014 |
| Link to Fulltext |
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