Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2016-1pp.39-45

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 51, Issue 1 / 2016 | Next article >>
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
<< Previous article | Volume 51, Issue 1 / 2016 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100