 | | 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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| Kh.Kh. Il'yasov, A.V. Kravtsov, S.V. Kuznetsov, and S.Ya. Sekerzh-Zen'kovich, "Exterior 3D Lamb Problem: Harmonic Load Distributed over a Surface," Mech. Solids. 51 (1), 39-45 (2016) |
| Year |
2016 |
Volume |
51 |
Number |
1 |
Pages |
39-45 |
| DOI |
10.3103/S0025654416010040 |
| Title |
Exterior 3D Lamb Problem: Harmonic Load Distributed over a Surface |
| Author(s) |
Kh.Kh. Il'yasov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, ilyasov@ipmnet.ru)
A.V. Kravtsov (Lomonosov Moscow State University, Moscow, 119992 Russia, avkravtsow@rambler.ru)
S.V. Kuznetsov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, kuzn-sergey@yandex.ru)
S.Ya. Sekerzh-Zen'kovich (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Financial University under the Government of the Russian Federation, Leningradskii pr. 49, Moscow, 125993 Russia, seker@ipmnet.ru) |
| Abstract |
The solutions of the exterior Lamb problem with a distributed harmonic surface load acting on the boundary of an elastic half-space are studied. A load normal to the surface and distributed over the surface as the Poisson kernel is considered. The solution is constructed with the use of integral transforms and the finite-element method. |
| Keywords |
Lamb problem, Poisson kernel, acoustic waves |
| References |
| 1. | H. Lamb,
"On the Propagation of Tremors over the Surface of an Elastic Solid,"
Phil. Trans. Roy. Soc. London. Ser. A
203 (359), 1-42 (1904). |
| 2. | H. Lamb,
"On Waves due to a Travelling Disturbance with an Application
to Waves in Superposed Fluids,"
Phil. Mag.
31 (4, 6), 386-399, 539-548 (1916). |
| 3. | W. M. Ewing, W. S. Jardetzki, F. Press,
Elastic Waves in Layered Media
(McGraw-Hill, New York, 1957). |
| 4. | L. Cagniard,
Reflexion et refraction des ondes seismiques progressives
(Gauthier-Villars, Paris, 1939). |
| 5. | A. T. De Hoop,
"A Modification of Cagniard's Method for Solving Seismic Pulse Problems,"
Appl. Sci. Res. Sect. Ser. B
8 (4), 349-356 (1960). |
| 6. | A. T. De Hoop,
"Theoretical Determination of the Surface Motion of a Uniform Elastic Half-Space
Produced by a Dilatational, Impulsive, Point Source,"
in La Propagation des Ebranlements dans les Milieux Heterogenes.
Colloq. Int. Centre Nat. Rech. Scient. (1961),
pp. 21-32. |
| 7. | C. L. Pekeris,
"The Seismic Surface Pulse,"
Proc. Nat. Acad. Sci. USA
41 (7), 469-480 (1955). |
| 8. | C. L. Pekeris,
"The Seismic Buried Pulse,"
Proc. Nat. Acad. Sci. USA
41 (9), 629-639 (1955). |
| 9. | V. I. Smirnov and S. L. Sobolev,
"On a New Method in the Plane Problem on Elastic Vibrations,"
Trudy Seismolog. Inst. AN SSSR,
No. 20 (1932)
[Tr. Seism. Inst. (French Transl.), No. 20 (1932);
in G. V. Demidenko and V. L. Vaskevich (Editors),
Selected Works of S. L. Sobolev, Volume I: Equations of Mathematical Physics, Computational Mathematics, and Cubature Formulas
(Springer, New York, 2006),
pp. 45-80 (Engl. Transl.)]. |
| 10. | V. I. Smirnov and S. L. Sobolev,
"On Application of a New Method to Study Elastic Vibrations in a Space with Axial Symmetry,"
Trudy Seismolog. Inst. AN USSR,
No. 29 (1933)
[Tr. Seism. Inst. (French Transl.), No. 29 (1933);
in G. V. Demidenko and V. L. Vaskevich (Editors),
Selected Works of S. L. Sobolev, Volume I: Equations of Mathematical Physics, Computational Mathematics, and Cubature Formulas
(Springer, New York, 2006),
pp. 81-130 (Engl. Transl.)] |
| 11. | G. I. Petrashen', G. I. Marchuk, and K. I. Ogurtsov,
"On Lamb's Problem for a Half-Space,"
Uch. Zap. Len. Gos. Univ., Ser. Mat.,
No. 21 (135), 71-118 (1950). |
| 12. | K. I. Ogurtsov and G. I. Petrashen',
"Dynamic Problems for Elastic Half-Space in the Case of Axial Symmetry,"
Uch. Zap. Len. Gos. Univ., Ser. Mat.,
No. 24 (149), 3-117 (1951). |
| 13. | R. J. Clifton,
"A Difference Method for Plane Problems in Dynamic Elasticity,"
Quart. Appl. Math.
25 (1), 97-116 (1967). |
| 14. | E. N. Vedenyapin and V. N. Kukudzhanov,
"A Method for the Numerical Integration of Nonstationary Problems
of the Dynamics of an Elastic Medium,"
Zh. Vychisl. Mat. Mat. Fiz.
21 (5), 1233-1248 (1981)
[USSR Comput. Math. Math. Phys. (Engl. Transl.)
21 (5), 160-174 (1981)]. |
| 15. | P. Moczo, E. Bystrický, J. Kristek et al.,
"Hybrid Modeling of P-SV Seismic Motion
at Inhomogeneous Viscoelastic Topographic Structures,"
Bull. Seismol. Soc. Am.
87 (5), 1305-1323 (1997). |
| 16. | A. V. Kravtsov, S. V. Kuznetsov, and S. Ya. Sekerzh-Zen'kovich,
"Finite Element Models in Lamb's Problem,"
Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 166-175 (2011)
[Mech. Solids (Engl. Transl.)
46 (6), 952-959 (2011)]. |
| 17. | E. M. Stein and N. J. Weiss,
"On the Convergence of Poisson Integrals,"
Trans. Am. Math. Soc.
140 (1), 35-54 (1969). |
|
| Received |
15 December 2013 |
| Link to Fulltext |
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