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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, Volume 9, Issue 2, Pages 317–337
DOI: https://doi.org/10.21638/spbu01.2022.212 (Mi vspua12) 		 
This article is cited in 3 scientific papers (total in 3 papers)

MECHANICS

Nonlinear modal interaction between longitudinal and bending vibrations of a beam resonator under periodic thermal loading

N. F. Morozovab, D. A. Indeitsevbc, A. V. Lukinc, I. A. Popovc, L. V. Shtukinbc

a St Petersburg State University, 7–9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
b Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, 61, V. O., Bolshoi pr., St Petersburg, 199178, Russian Federation
c Peter the Great St Petersburg Polytechnic University, 29, ul. Polytechnicheskaya, St Petersburg, 195251, Russian Federation
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DOI: https://doi.org/10.21638/spbu01.2022.212
Abstract: The paper investigates the nonlinear modal interaction of longitudinal and bending vibrations of a beam resonator under periodic thermal loading. The mode of parametric oscillations is investigated under conditions of internal multiple resonance between some flexural and longitudinal forms of free oscillations of the resonator. The possibility of generation in the system of the longitudinal-bending mode was found, the frequency of the slow envelope of which essentially depends on the parameter of the internal frequency detuning, which is directly related to the magnitude of external disturbances subject to high-precision measurement.
Keywords: nonlinear dynamics, parametric oscillations, Bernoulli — Euler beam, modal interaction, beats.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00537
This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00537).
Received: 18.10.2021
Revised: 26.11.2021
Accepted: 02.12.2021
English version:
Vestnik St. Petersburg University, Mathematics, 2022, Volume 9, Issue 2, Pages 317–337
DOI: https://doi.org/10.1134/S106345412202008X
Bibliographic databases:
Document Type: Article
UDC: 534.11
MSC: 74H60
Language: Russian
Citation: N. F. Morozov, D. A. Indeitsev, A. V. Lukin, I. A. Popov, L. V. Shtukin, “Nonlinear modal interaction between longitudinal and bending vibrations of a beam resonator under periodic thermal loading”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9:2 (2022), 317–337; Vestn. St. Petersbg. Univ., Math., 9:2 (2022), 317–337
Citation in format AMSBIB
\Bibitem{MorIndLuk22}
\by N.~F.~Morozov, D.~A.~Indeitsev, A.~V.~Lukin, I.~A.~Popov, L.~V.~Shtukin
\paper Nonlinear modal interaction between longitudinal and bending vibrations of a beam resonator under periodic thermal loading
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2022
\vol 9
\issue 2
\pages 317--337
\mathnet{http://mi.mathnet.ru/vspua12}
\crossref{https://doi.org/10.21638/spbu01.2022.212}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4458045}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2022
\vol 9
\issue 2
\pages 317--337
\crossref{https://doi.org/10.1134/S106345412202008X}
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    • This publication is cited in the following 3 articles:
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