Abstract:
Explicit presentations for the initial terms of the asymptotic solution of the spectral problem of the elasticity theory in a plane region with a rapidly oscillating boundary are obtained. Based on asymptotic formulas, two methods for problem modeling are proposed: with the use of Wenzel’s boundary conditions and with the use of the principle of a smooth image of a singularly perturbed boundary. Various approaches to justification of asymptotic presentations are discussed.
Citation:
S. A. Nazarov, “Eigenoscillations of an elastic body with a rough surface”, Prikl. Mekh. Tekh. Fiz., 48:6 (2007), 103–114; J. Appl. Mech. Tech. Phys., 48:6 (2007), 861–870
\Bibitem{Naz07}
\by S.~A.~Nazarov
\paper Eigenoscillations of an elastic body with a rough surface
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2007
\vol 48
\issue 6
\pages 103--114
\mathnet{http://mi.mathnet.ru/pmtf2098}
\elib{https://elibrary.ru/item.asp?id=17425765}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2007
\vol 48
\issue 6
\pages 861--870
\crossref{https://doi.org/10.1007/s10808-007-0110-z}
Linking options:
https://www.mathnet.ru/eng/pmtf2098
https://www.mathnet.ru/eng/pmtf/v48/i6/p103
This publication is cited in the following 3 articles:
Saoussen Boujemaa, Abdessatar Khelifi, “Asymptotic expansion for solution of Maxwell equation in domain with highly oscillating boundary”, Z Angew Math Mech, 103:10 (2023)
Siwar Saidani, Abdessatar Khelifi, “Eigenoscillations of the Maxwell equation in a domain with oscillating boundary”, Complex Variables and Elliptic Equations, 2023, 1
D. Gómez, S. A. Nazarov, M. E. Pérez, “Homogenization of Winkler–Steklov spectral conditions in three-dimensional linear elasticity”, Z. Angew. Math. Phys., 69:2 (2018)
Citation in format AMSBIB
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