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S.V. Kuznetsov and E.O. Terent'eva, "Wave Fields and Domination Regions for the Interior Lamb Problem," Mech. Solids. 50 (5), 508-520 (2015) |
Year |
2015 |
Volume |
50 |
Number |
5 |
Pages |
508-520 |
DOI |
10.3103/S0025654415050039 |
Title |
Wave Fields and Domination Regions for the Interior Lamb Problem |
Author(s) |
S.V. Kuznetsov (A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, kuzn-sergey@yandex.ru)
E.O. Terent'eva (Moscow State University of Civil Engineering, Yaroslavskoe sh. 26, Moscow, 129337 Russia) |
Abstract |
The domination regions of wave fields in the epicentral region are analyzed for the interior Lamb problem on the action of a lumped force applied inside an elastic half-plane. The solutions obtained by integral representations and finite-element approximations are compared. The domination regions are distinguished for the first time for all types of acoustic waves observed near the epicenter. |
Keywords |
Lamb problem, surface wave, decaying wave, epicenter |
References |
1. | H. Lamb,
"On the Propagation of Tremors over the Surface of an Elastic Solid,"
Phil. Trans. Roy. Soc. London
203, 1-42 (1904). |
2. | H. Lamb,
"On Waves due to a Travelling Disturbance with an Application to Waves in Superposed Fluids,"
Phil. Mag.
13, 386-399, 539-548 (1916). |
3. | W. M. Ewing, W. S. Jardetzky, and F. Press,
Elastic Waves in Layered Media
(McGraw-Hill, New York, 1957). |
4. | J. W. Strutt,
"On Wave Propagating along the Plane Surface of an Elastic Solid,"
Proc. London Math. Soc.
17, 4-11 (1885). |
5. | M. E. Gurtin,
The Linear Theory of Elasticity,
in Handbuch der Physik, Vol. VIa/II
(Springer, 1972). |
6. | H. Nakano,
"Some Problems Concerning the Propagation of the Distrubances
in and on Semi-Infinite Elastic Solid,"
Geophys. Mag.
2, 189-348 (1930). |
7. | H. Nakano,
"On Rayleigh Waves,"
Japan J. Astron. Geophys.
2, 233-326 (1925). |
8. | E. R. Lapwood,
"The Disturbance due to a Line Source in a Semi-Infinite Elastic Medium,"
Phil. Trans. Roy. Soc. London. Ser. A
242, 63-100 (1949). |
9. | L. Cagniard,
Reflexion et Refraction des Ondes Seismiques Progressives
(Gauthier-Villars, Paris, 1939). |
10. | 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). |
11. | 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 Milieus Heterogenes.
Colloques Internationaux du Centre National de la Recherche Scientique
(Marseille, 1961),
pp. 21-32. |
12. | W. W. Garvin,
"Exact Transient Solution of the Buried Line Source Problem,"
Proc. Roy. Soc.
234, 528-541 (1956). |
13. | F. Sanchez-Sesma and U. Iturraran-Viveros,
"The Classic Garvin's Problem Revisited,"
Bull. Seismol. Soc. Am.
96, 1344-1351 (2006). |
14. | F. Sanchez-Sesma, U. Iturraran-Viveros, and E. Kausel,
"Garvin's Generalized Problem Revisited,"
Soil Dyn. Earthq. Engng
47, 4-15 (2013). |
15. | D. P. Williams and R. V. Craster,
"Cagniard-de Hoop Path Perturbations with Applications
to Nongeometric Wave Arrivals,"
J. Engng Math.
37, 253-272 (2000). |
16. | C. L. Pekeris,
"The Seismic Surface Pulse,"
Proc. Nat. Acad. Sci. USA
41, 469-480 (1955). |
17. | C. L. Pekeris,
"The Seismic Buried Pulse,"
Proc. Nat. Acad. Sci. USA
41, 629-639 (1955). |
18. | C. L. Pekeris and H. Lifson,
"Motion of the Surface of a Uniform Elastic Half-Space Produced
by a Buried Pulse,"
J. Acoust. Soc. Am.
29, 1233-1238 (1957). |
19. | C. L. Pekeris and I. M. Longman,
"The Motion of the Surface of a Uniform Elastic Half-Space Produced by a Buried Torque-Pulse,"
Geophys. J.
1, 146-153 (1958). |
20. | C. L. Pekeris, F. Abramovici, and Z. Alterman,
"Propagation of an SH-Torque Pulse in a Layered Solid,"
Bull. Seismol. Soc. Am.
53, 39-57 (1963). |
21. | E. Pinney,
"Surface Motion due to a Point Source in a Semi-Infinite Elastic Meidum,"
Bull. Seismol. Soc. Am.
44, 571-596 (1954). |
22. | R. G. Payton,
"Transient Motion of an Elastic Half-Space due to a Moving Surface Line Load,"
Int. J. Engng Sci.
5, 49-79 (1967). |
23. | R. G. Payton,
"Epicenter Motion of an Elastic Half-Space due to Buried Stationary and Moving Line Sources,"
Int. J. Solids Struct.
4, 287-300 (1968). |
24. | R. G. Payton,
"Epicenter Motion of a Transversely Isotropic Elastic Half-Space
due to a Suddenly Applied Buried Point Source,"
Int. J. Engng Sci.
17, 879-887 (1979). |
25. | L. R. Johnson,
"Green's Function for Lamb's Problem,"
Geophys. J. Roy. Astron. Soc.
37, 99-131 (1974). |
26. | R. Sato,
"Seismic Waves in the Near Field,"
J. Phys. Earth.
20, 357-375 (1972). |
27. | I. Kawasaki, Y. Suzuki, and R. Sato,
"Seismic Waves due to Double Couple Source in a Semi-Infinite Space. Part 1,"
Zisin.
25, 207-217 (1972). |
28. | I. Kawasaki, Y. Suzuki, and R. Sato,
"Seismic Waves due to Double Couple Source in a semi-Infinite Space. Part 2,"
Zisin.
25, 333-342 (1972). |
29. | E. Kausel,
Fundamental Solutions of Elastodynamics
(Cambridge Univ. Press., New York, 2006). |
30. | G. I. Petrashen',
"On Lamb's Problem for an Elastic Half-Space,"
Dokl. Akad. Nauk SSSR
64 (5), 649-652 (1949). |
31. | 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). |
32. | 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). |
33. | N. I. Onis'ko and E. I. Shemyakin,
"Motion of Free Surface of Homogeneous Soil due to Underground Explosion,"
Zh. Prikl. Mekh. Tekhn. Fiz.,
No. 4, 82-93 (1961)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)]. |
34. | 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.)]. |
35. | 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.)] |
36. | P. D. Lax and B. Wendroff,
"Difference Schemes for Hyperbolic Equations with High Order of Accuracy,"
Comm. Pure Appl. Math.
17, 381-398 (1964). |
37. | B. Wendroff,
Theoretical Numerical Analysis
(Academic Press, New York, 1967). |
38. | B. A. Finlayson,
Numerical Methods for Problems with Moving Fronts
(Ravenna Park Pub, 1992). |
39. | N. Holmes and T. Belytschko,
"Postprocessing of Finite Element Transient Response Calculations by Digital Filters,"
Comp. Struct.
6, 211-216 (1976). |
40. | P. Moczo, E. Bystrick'y, J. Kristek, et al.,
"Hybrid Modeling of P-SV Seismic Motion at Inhomogeneous Viscoelastic Topographic Structures,"
Bull. Seism. Soc. Am.
87 (5), 1305-1323 (1997). |
41. | A. R. Levander,
"Fourth-Order Finite-Difference P-SV Seismographs,"
Geophys.
53, 1425-1436 (1988). |
42. | P. Moczo, J. Kristek, V. Vavrycuk, et al.,
"3D Heterogeneous Staggered-Grid Finite-Difference Modeling of Seismic Motion
with Volume Harmonic and Arithmetic Averaging of Elastic Moduli and Densities,"
Bull. Seism. Soc. Am.
92 (8), 3042-3066 (2002). |
43. | M. Shuo, R. J. Archuleta, and P. Liu,
"Hybrid Modeling of Elastic P-SV Wave Motion: A Combined Finite-Element
and Staggered-Grid Finite-Difference Approach,"
Bull. Seism. Soc. Am.
94 (4), 1557-1563 (2004). |
44. | A. V. Kravtsov, S. V. Kuznetsov, and S. Ya. Sekerzh-Zen'kovich,
"Finite Element Models in Lamb's Problem,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 160-169 (2011)
[Mech. Solids (Engl. Transl.)
46 (6), 952-959 (2011)]. |
|
Received |
01 April 2014 |
Link to Fulltext |
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