 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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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,
"Problems in Wave Propagation in Soil and Rocks,"
in Proc. of the Intern. Symposium on Wave Propagation
and Dynamic Properties of Earth Materials, New Mexico, USA
(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,
"On the Action of Seismic Wave on Underground Pipelines,"
Izv. Akad. Nauk UzSSR. Ser. Tekhn. Nauk, No. 1, 37-42 (1971);
in A. A. Il'yushin,
Collected Works,
Vol. 4: Modeling of Dynamic Processes in Solids and Engineering Applications
(Fizmatlit, Moscow, 2009)
[in Russian]. |
| 4. | M. Sh. Israilov,
"Seismiodynamics of an Underground Pipeline,"
in Proc. of the 15th World. Conf. on Earth. Engng (15WCEE), Lissabon, Portugal
(2012),
p. 2125. |
| 5. | M. Sh. Israilov,
"Seismiodynamics of an Underground Pipeline,"
Probl. Mekh. Akad. Nauk RUz,
No. 3, 18-24 (2012). |
| 6. | K. Toki and S. Takada,
"Earthquake Response Analysis of Underground Tubular Structure,"
Bull. Disas. Prev. Res. Inst. Kyoto Univ.
24(2) (221), 107-125 (1974). |
| 7. | M. Sh. Israilov,
"Reduction of Boundary Value Problems of Dynamic Elasticity
to Scalar Problems for Wave Potentials in Curvilinear Coordinates,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
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,
Ed. by I. N. Aneddon and R. Hill
(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,
"Differential Equation of Underground Pipeline Vibrations during Earthquakes,"
Dokl. Akad. Nauk UzSSR,
No. 9, 10-12 (1962). |
| 12. | M. A. Biot,
"Propagation of Elastic Waves in a Cylindrical Bore Containing a Fluid,"
J. Appl. Phys. 23 (9), 997-1005 (1952);
in Collection of Translations "Mechanics",
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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