Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2011, Volume 11, Issue 3(1), Pages 61–89
This article is cited in 1 scientific paper (total in 1 paper)
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
The structural algorithm of the finite integral transformation method is presented as a generalization of the classical procedure of eigenvector decomposition. The initial-boundary problems described with a hyperbolic system of linear partial second order differential equations are considered. The general case of non-self adjoint solution by expansion in the vector-functions is possible only by the use of biorthogonal of finite integral transformations. In particular, for self-adjoint initial-boundary 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 three-layer anisotropic elastic cylindrical shell under the general conditions of loading and fastening on the circuit.
method, generalized algorithm, finite integral transformations, multicomponent ability, biorthogonality, special decomposition, vector-functions, boundary value problems, self-adjoint, non-self adjointness, hyperbolic equations, solution existence, convergency, singularity, integrality, cylindrical shell, tri-plies, refined theory, closed solution.
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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
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\paper Finite integral transformations method~-- generalization of classic procedure for eigenvector decomposition
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
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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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