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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 139, Pages 59–69 (Mi into224)  
Solution of periodic boundary-value problems of the spatial theory of elasticity in the vector form

E. A. Osipov

Kazan (Volga Region) Federal University
Full-text PDF (174 kB)
Abstract: We discuss boundary-value problems for the system of equations of the spatial theory of elasticity in the class of double-periodic functions and obtain a general solution of the system. We distinguish six types of elementary Floquet waves and examine their energy characteristics. We consider fundamental boundary-value problems in the half-space in the vector form. The diffraction problem for an elastic wave on a periodic system of defects in the vector form is reduced to the paired summator functional equation.
Keywords: periodic system, theory of elasticity, Floquet wave.
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 3, Pages 306–317
DOI: https://doi.org/10.1007/s10958-019-04425-4
Bibliographic databases:
Document Type: Article
UDC: 517.912, 517.958:539.3(3)
MSC: 74B05
Language: Russian
Citation: E. A. Osipov, “Solution of periodic boundary-value problems of the spatial theory of elasticity in the vector form”, Differential equations. Mathematical physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 139, VINITI, M., 2017, 59–69; Journal of Mathematical Sciences, 241:3 (2019), 306–317
Citation in format AMSBIB
\Bibitem{Osi17}
\by E.~A.~Osipov
\paper Solution of periodic boundary-value problems of the spatial theory of elasticity in the vector form
\inbook Differential equations. Mathematical physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 139
\pages 59--69
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into224}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3799906}
\zmath{https://zbmath.org/?q=an:1427.74022}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 3
\pages 306--317
\crossref{https://doi.org/10.1007/s10958-019-04425-4}
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