S. D. Algazin, I. A. Selivanov, “Problem of eigen-vibrations of a rectangular plate with mixed border conditions”, Prikl. Mekh. Tekh. Fiz., 62:2 (2021), 70–76; J. Appl. Mech. Tech. Phys., 62:2 (2021), 238

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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Volume 62, Issue 2, Pages 70–76
DOI: https://doi.org/10.15372/PMTF20210207 (Mi pmtf189)

This article is cited in 9 scientific papers (total in 9 papers)

Problem of eigen-vibrations of a rectangular plate with mixed border conditions

S. D. Algazin^a, I. A. Selivanov^b

^a Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, 119526, Moscow, Russia
^b Lomonosov Moscow State University, 119991, Moscow, Russia

Full-text PDF (305 kB) Citations (9)

DOI: https://doi.org/10.15372/PMTF20210207

Abstract: Natural vibrations of a rectangular plate with two pinched and two freely supported edges. The Bubnov method – Galerkin methods are used to obtain the first eigenvalues, and one of the test functions has its first eigenvalue calculated with an error smaller than 1%. Comparison with known results is carried out, with eigenforms given.

Keywords: biharmonic equation, free vibrations of a plate, method Bubnova–Galerkina, computational experiment.

Funding agency	Grant number
Ministry of Science and Higher Education of the Russian Federation	АААА-А20-120011690132-4

Received: 21.04.2020
Revised: 03.06.2020
Accepted: 29.06.2020

English version:
Journal of Applied Mechanics and Technical Physics, 2021, Volume 62, Issue 2, Pages 238–244
DOI: https://doi.org/10.1134/S0021894421020073

Bibliographic databases:

Document Type: Article

UDC: 539.3:534.1

Language: Russian

Citation: S. D. Algazin, I. A. Selivanov, “Problem of eigen-vibrations of a rectangular plate with mixed border conditions”, Prikl. Mekh. Tekh. Fiz., 62:2 (2021), 70–76; J. Appl. Mech. Tech. Phys., 62:2 (2021), 238–244

Citation in format AMSBIB

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\paper Problem of eigen-vibrations of a rectangular plate with mixed border conditions

\jour Prikl. Mekh. Tekh. Fiz.

\yr 2021

\vol 62

\issue 2

\pages 70--76

\mathnet{http://mi.mathnet.ru/pmtf189}

\crossref{https://doi.org/10.15372/PMTF20210207}

\elib{https://elibrary.ru/item.asp?id=45600943}

\transl

\jour J. Appl. Mech. Tech. Phys.

\yr 2021

\vol 62

\issue 2

\pages 238--244

\crossref{https://doi.org/10.1134/S0021894421020073}

Linking options:

https://www.mathnet.ru/eng/pmtf189

https://www.mathnet.ru/eng/pmtf/v62/i2/p70

This publication is cited in the following 9 articles:

V. N. Paimushin, V. M. Shishkin, A. N. Nuriev, S. F. Chumakova, “Study of the Dynamic Behavior of a Rod-Strip Based on a Transformational Model of Deformation with Specified Displacements of the Support Element. Theory and Experiment”, Mech Compos Mater, 2025
V. N. Paimushin, V. M. Shishkin, “A refined model of dynamic deformation of a rod-strip with a fixed section of a finite length on one of the facial surfaces”, J. Appl. Mech. Tech. Phys., 65:1 (2024), 161–175
V. N. Paimushin, V. M. Shishkin, S. F. Chumakova, “Forced Bending Vibrations of a Plane Rod Fixed on a Rigid Support Element of Finite Length Under the Action of an External Transverse Force Aplied to Its Free End”, Mech Compos Mater, 60:3 (2024), 501
V. N. Paimushin, V. M. Shishkin, S. F. Chumakova, “Mathematical Modeling of the Dynamic Deformation of a Rod-Strip Fixed on a Double-Sided Support Element through Elastic Interlayers”, jour, 166:3 (2024), 407
V. N. Paimushin, V. M. Shishkin, “The simplest transformation model of deformation of a rod-strip fixed on a double-sided support element through elastic interlayers”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 10, 98–106
V. N. Paimushin, “Two variants of stating problems of mechanics of a rod-strip with a section of one-sided fixing of finite length on a rigid support element”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 11, 88–96
V. N. Paimushin, V. M. Shishkin, “The Simplest Transformation Model of Deformation of a Strip Fixed on a Double-Sided Support Element via Elastic Interlayers”, Russ Math., 68:10 (2024), 85
V. N. Paimushin, “Two Variants of Stating Problems of Mechanics of a Strip with a Section of One-Sided Fixing of Finite Length on a Rigid Support Element”, Russ Math., 68:11 (2024), 77
S. D. Algazin, I. A. Selivanov, “Plate flutter problem with mixed boundary conditions”, J. Appl. Mech. Tech. Phys., 63:5 (2022), 869–875

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Prikladnaya Mekhanika i Tekhnicheskaya Fizika

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