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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2011, Volume 11, Issue 2, Pages 83–96
DOI: https://doi.org/10.18500/1816-9791-2011-11-2-83-96 (Mi isu222) 		 
Mechanics

Mode-series expansion of solutions of elasticity problems for a strip

L. Yu. Kossovicha, V. A. Yurkob, I. V. Kirillovac

a Saratov State University, Chair of Mathematical Theory of Elasticity and Biomechanics
b Saratov State University, Chair of Mathematical Physics and Numerical Analysis
c Educational-Research Institute of Nanostructures and Biosystems
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DOI: https://doi.org/10.18500/1816-9791-2011-11-2-83-96
Abstract: Oscillations of a strip are considered as a plane problem of elasticity theory. Description of oscillation modes is provided. Properties of eigenvalues and eigenfunctions are studied for a boundary value problem for their amplitudes. Green's function is constructed as a kernel of the inverse operator. Completeness and expansion theorems are proved which allow one to solve problems for finite and infinite membranes under arbitrary boundary conditions.
Key words: elasticity theory, wave propagation, oscillation modes, eigenvalues, eigenfunctions.
Document Type: Article
UDC: 539.3
Language: Russian
Citation: L. Yu. Kossovich, V. A. Yurko, I. V. Kirillova, “Mode-series expansion of solutions of elasticity problems for a strip”, Izv. Saratov Univ. Math. Mech. Inform., 11:2 (2011), 83–96
Citation in format AMSBIB
\Bibitem{KosYurKir11}
\by L.~Yu.~Kossovich, V.~A.~Yurko, I.~V.~Kirillova
\paper Mode-series expansion of solutions of elasticity problems for a~strip
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2011
\vol 11
\issue 2
\pages 83--96
\mathnet{http://mi.mathnet.ru/isu222}
\crossref{https://doi.org/10.18500/1816-9791-2011-11-2-83-96}
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    		Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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