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
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.
.
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
\Bibitem{Kar20}
\by A.~L.~Karchevsky
\paper 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
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 4
\pages 48--68
\mathnet{http://mi.mathnet.ru/sjim1108}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.404}
\elib{https://elibrary.ru/item.asp?id=44752279}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 4
\pages 648--665
\crossref{https://doi.org/10.1134/S1990478920040043}
\elib{https://elibrary.ru/item.asp?id=44967504}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85100219592}
Linking options:
https://www.mathnet.ru/eng/sjim1108
https://www.mathnet.ru/eng/sjim/v23/i4/p48
This publication is cited in the following 12 articles:
U. D. Durdiev, “Obratnaya zadacha ob istochnike dlya uravneniya vynuzhdennykh kolebanii balki”, Izv. vuzov. Matem., 2023, no. 8, 10–22
U. D. Durdiev, Z. R. Bozorov, “Nonlocal inverse problem for determining the unknown coefficient in the beam vibration equation”, J. Appl. Industr. Math., 17:2 (2023), 281–290
U. D. Durdiev, “Inverse Source Problem for the Equation of Forced Vibrations of a Beam”, Russ Math., 67:8 (2023), 7
U. D Durdiev, “Nelokal'naya obratnaya zadacha po vremeni dlya uravneniya kolebaniy balki s integral'nym usloviem”, Differentsialnye uravneniya, 59:3 (2023), 358
U. D. Durdiev, “A Time-Nonlocal Inverse Problem for the Beam Vibration Equation with an Integral Condition”, Diff Equat, 59:3 (2023), 359
U. D. Durdiev, “Inverse Problem of Determining the Unknown Coefficient in the Beam Vibration Equation in an Infinite Domain”, Diff Equat, 59:4 (2023), 462
M. V. Neschchadim, A. A. Simonov, “Backlund transformations of the relativistic Schrodinger equation”, J. Appl. Industr. Math., 17:4 (2023), 828–841
Yu. E. Anikonov, M. V. Neschadim, A. P. Chupakhin, “Mnogomernoe uravnenie Khopfa i nekotorye ego tochnye resheniya”, Sib. zhurn. industr. matem., 25:1 (2022), 5–13
Yu. E. Anikonov, M. V. Neshchadim, A. P. Chupakhin, “Multidimensional Hopf Equation and Some of Its Exact Solutions”, J. Appl. Ind. Math., 16:1 (2022), 1
U. D. Durdiev, “Inverse Problem of Determining an Unknown Coefficient in the Beam Vibration Equation”, Diff Equat, 58:1 (2022), 36
M. V. Neshchadim, A. P. Chupakhin, “Method of commutators for integration of a matrix Riccati equation”, J. Appl. Industr. Math., 15:1 (2021), 78–86
M. V. Neshchadim, A. P. Chupakhin, “On integration of a matrix Riccati equation”, J. Appl. Industr. Math., 14:4 (2020), 732–742
Citation in format AMSBIB
Contact us: