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Sibirskii Zhurnal Industrial'noi Matematiki, 2020, Volume 23, Number 4, Pages 48–68
DOI: https://doi.org/10.33048/SIBJIM.2020.23.404 (Mi sjim1108) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Analytical solutions to the differential equation of transverse vibrations of a piecewise homogeneous beam in the frequency domain for the boundary conditions of various types

A. L. Karchevsky

Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
Full-text PDF (636 kB) Citations (12)
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DOI: https://doi.org/10.33048/SIBJIM.2020.23.404
Abstract: We obtain an analytical solution for the differential equation of transverse vibrations of a piecewise homogeneous beam in the frequency domain for various types of boundary conditions. All calculations involved are addition, multiplication, and inversion of square matrices of second order. The formulas are such that, when using them for layer-by-layer recalculation, the rounding error does not accumulate since the exponential functions in some expressions have exponents with nonpositive real parts.
Keywords: equation of transverse vibrations of a beam, layer-by-layer recalculation. .
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314-2019-0011
The author was supported by the State Task to the Sobolev Institute of Mathematics (project no. 0314-2019-0011).
Received: 10.06.2020
Revised: 31.07.2020
Accepted: 10.09.2020
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 4, Pages 648–665
DOI: https://doi.org/10.1134/S1990478920040043
Bibliographic databases:
Document Type: Article
UDC: 519.624.3
Language: Russian
Citation: A. L. Karchevsky, “Analytical solutions to the differential equation of transverse vibrations of a piecewise homogeneous beam in the frequency domain for the boundary conditions of various types”, Sib. Zh. Ind. Mat., 23:4 (2020), 48–68; J. Appl. Industr. Math., 14:4 (2020), 648–665
Citation in format AMSBIB
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\vol 23
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\pages 48--68
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\jour J. Appl. Industr. Math.
\yr 2020
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\pages 648--665
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский журнал индустриальной математики
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