Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
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ISSN 0021-8928
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IssuesArchive of Issues2009-1pp.63-70

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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
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