 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10482 |
| In Russian (ΟΜΜ): | | 9683
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| In English (J. Appl. Math. Mech.): | | 799 |
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| Ye.A. Shirokova, "The interpolation solution of the second basic plane problem of the dynamics of elastic solids," J. Appl. Math. Mech. 73 (1), 63-70 (2009) |
| Year |
2009 |
Volume |
73 |
Issue |
1 |
Pages |
63-70 |
| Title |
The interpolation solution of the second basic plane problem of the dynamics of elastic solids |
| Author(s) |
Ye.A. Shirokova (Kazan, Russia, elena.shirokova@ksu.ru) |
| Abstract |
The second basic plane problem of the dynamics of elastic bodies is considered in the Muskhelishvili formulation, when the known boundary displacements are replaced by interpolation time polynomials and the known initial conditions are replaced by polyharmonic functions, which interpolate the initial conditions in a region with a finite number of interpolation nodes. In this case a solution of the problem, called here the interpolation solution, is possible. It must satisfy the dynamic equations and interpolate the boundary displacements and initial displacements and velocities. This solution is constructed in the form of a polynomial and is reduced to solving a series of boundary-value problems for determining the coefficients of this polynomial. |
| References |
| 1. | N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen (1953). |
| 2. | Berezin I S, Zhidkov N P. Computing Methods. Vol. 1. Oxford: Pergamon; 1965. |
| 3. | V.K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials, Nauka, Moscow (1977). |
| 4. | Privalov I. and Pchelin B.K. The general theory of polyharmonic functions. Mat Sbornik 2(44); No. 4, 745–58: 1937. |
|
| Received |
13 December 2007 |
| Link to Fulltext |
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