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Russian Journal of Nonlinear Dynamics, 2020, Volume 16, Number 2, Pages 309–324
DOI: https://doi.org/10.20537/nd200206
(Mi nd712)
 

This article is cited in 2 scientific papers (total in 2 papers)

Nonlinear physics and mechanics

Mathematical Study of the Small Oscillations of a Pendulum Completely Filled with a Viscoelastic Fluid

H. Essaouinia, P. Capodannob

a Abdelmalek Essaâdi University, Faculty of Sciences, M2SM ER28/FS/05, 93030 Tetuan, Morocco
b Université de Franche-Comté, 2B — Rue des jardins, 25000 Besancon, France
Full-text PDF (265 kB) Citations (2)
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Abstract: We study the small oscillations of a pendulum completely filled by a viscoelastic fluid, restricting ourselves for the fluid to the simpler Oldroyd model. We establish the equations of motion of the system. Writing them in a suitable form, we obtain an existence and unicity theorem of the solution of the associated evolution problem by means of semigroup theory. Afterwards, we show the existence and symmetry of the spectrum and prove the stability of the system. We show the existence of two sets of positive real eigenvalues, of which the first has infinity, and the second a point of the real axis, as points of accumulation. Finally, we specify the location of the possible nonreal eigenvalues.
Keywords: viscoelastic fluid, small oscillations, variational-operatorial and spectral methods, semigroups.
Received: 25.09.2019
Accepted: 30.03.2020
Bibliographic databases:
Document Type: Article
Language: English
Citation: H. Essaouini, P. Capodanno, “Mathematical Study of the Small Oscillations of a Pendulum Completely Filled with a Viscoelastic Fluid”, Rus. J. Nonlin. Dyn., 16:2 (2020), 309–324
Citation in format AMSBIB
\Bibitem{EssCap20}
\by H.~Essaouini, P.~Capodanno
\paper Mathematical Study of the Small Oscillations of a Pendulum Completely Filled with a Viscoelastic Fluid
\jour Rus. J. Nonlin. Dyn.
\yr 2020
\vol 16
\issue 2
\pages 309--324
\mathnet{http://mi.mathnet.ru/nd712}
\crossref{https://doi.org/10.20537/nd200206}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85093900049}
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  • This publication is cited in the following 2 articles:
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    Russian Journal of Nonlinear Dynamics
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