
Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2011, Volume 11, Issue 3(1), Pages 61–89
(Mi isu236)




This article is cited in 1 scientific paper (total in 1 paper)
Mechanics
Finite integral transformations method – generalization of classic procedure for eigenvector decomposition
Yu. E. Senitsky^{} ^{} Samara State University of Architecture and Civil Engineering, Chair of Resistance of Materials and Construction Mechanics
Abstract:
The structural algorithm of the finite integral transformation method is presented as a generalization of the classical procedure of eigenvector decomposition. The initialboundary problems described with a hyperbolic system of linear partial second order differential equations are considered. The general case of nonself adjoint solution by expansion in the vectorfunctions is possible only by the use of biorthogonal of finite integral transformations. In particular, for selfadjoint initialboundary problems solutions obtained by the method of finite integral transforms and the classic procedure of eigenvector decomposition expansion are identical, although the first of these is preferable. These statements are illustrated by the example of a closed solution of the dynamic problem for a threelayer anisotropic elastic cylindrical shell under the general conditions of loading and fastening on the circuit.
Key words:
method, generalized algorithm, finite integral transformations, multicomponent ability, biorthogonality, special decomposition, vectorfunctions, boundary value problems, selfadjoint, nonself adjointness, hyperbolic equations, solution existence, convergency, singularity, integrality, cylindrical shell, triplies, refined theory, closed solution.
DOI:
https://doi.org/10.18500/18169791201111316189
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UDC:
517.958
Citation:
Yu. E. Senitsky, “Finite integral transformations method – generalization of classic procedure for eigenvector decomposition”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 11:3(1) (2011), 61–89
Citation in format AMSBIB
\Bibitem{Sen11}
\by Yu.~E.~Senitsky
\paper Finite integral transformations method~ generalization of classic procedure for eigenvector decomposition
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2011
\vol 11
\issue 3(1)
\pages 6189
\mathnet{http://mi.mathnet.ru/isu236}
\crossref{https://doi.org/10.18500/18169791201111316189}
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This publication is cited in the following articles:

Bespalova E.I., “Generalized Method of Finite Integral Transforms in Static Problems For Anisotropic Prisms”, Int. Appl. Mech., 54:1 (2018), 41–55

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