 | | 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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| A. G. Bagdoev, A. N. Martirosyan, G. A. Martirosyan, and S. M. Pogosyan, "Solution of a mixed dynamic problem on the displacements given on the boundary of a half-plane lying on the surface of an isotropic homogeneous elastic half-space," Mech. Solids. 42 (1), 57-63 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
1 |
Pages |
57-63 |
| Title |
Solution of a mixed dynamic problem on the displacements given on the boundary of a half-plane lying on the surface of an isotropic homogeneous elastic half-space |
| Author(s) |
A. G. Bagdoev (Institute of Mechanics, National Academy of Sciences of the Republic of Armenia, pr-t Marshla Baghramiana 24B, Yerevan, 375019, Republic of Armenia, mechins@sci.am)
A. N. Martirosyan (Goris State University, Avangardi 4, Goris, Syunik Marz, 3204, Republic of Armenia, seuagoris@mail.ru)
G. A. Martirosyan (Goris State University, Avangardi 4, Goris, Syunik Marz, 3204, Republic of Armenia)
S. M. Pogosyan (Goris State University, Avangardi 4, Goris, Syunik Marz, 3204, Republic of Armenia, sam41po@rambler.ru) |
| Abstract |
We consider the problem on the motion of an isotropic elastic body occupying the half-space z≥0 on whose boundary, along the half-plane x≥0, the horizontal components of displacement are given, while the remaining part of the boundary is stress-free. We seek the solution by the method of integral Laplace transforms with respect to time t and Fourier transforms with respect to the coordinates x, y; the problem is reduced to a system of Wiener-Hopf equations, which can be solved by the methods of singular-integral equations and circulants. We invert the integral transforms and reduce the solution to the Smirnov-Sobolev form. We calculate the tangential stress intensity coefficients near the boundary z=0, x=0, |y|<∞ of the half-plane. The circulant method for solving the Wiener-Hopf system was proposed in [1]. A static problem similar to that considered in the present paper was solved earlier. The Hilbert problem was reduced to a system of Fredholm integral equations in [2]. In the present paper, we solve the above problem by reducing the solution to quadratures and a quasiregular system of Fredholm integral equations. We give a numerical solution of the Fredholm equations and calculate the integrals for the tangential stress intensity coefficients. |
| References |
| 1. | V. S. Sarkisyan and I. M. Karakhanyan,
"Diffraction of Shear Elastic Harmonic Waves on Half-Infinite Inclusions,"
in Problems of Mechanics of Thin Bodies. Dedicated to the 80th Anniversary
of S. A. Ambartsumyan, Academician of Armenian NAS
(Erevan, 2002), pp. 266-280
[in Russian] |
| 2. | N. P. Vekua,
Systems of Singular Integral Equations and Some Boundary Value Problems
(Nauka, Moscow, 1970)
[in Russian]. |
| 3. | B. Noble,
Methods Based on the Wiener-Hopf Technique for the Solution of Partial
Differential Equations
(Izd-vo Inostr. Lit., Moscow, 1962)
[in Russian]. |
| 4. | A. N. Martirosyan,
"Solution of a Mixed Dynamic Boundary Value Problem for an Elastic Half-Space,"
Inform. Tekhnologii i Upravlenie,
No. 3 (2003). |
|
| Received |
05 October 2004 |
| Link to Fulltext |
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