Russian Journal of Nonlinear Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Rus. J. Nonlin. Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Rus. J. Nonlin. Dyn., 2020, Volume 16, Number 2, Pages 309–324 (Mi nd712)  

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

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

DOI: https://doi.org/10.20537/nd200206

Full text: PDF file (265 kB)
References: PDF file   HTML file

MSC: 76A10, 76M22, 76M30, 49R05, 47A75
Received: 25.09.2019
Accepted:30.03.2020
Language:

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}


Linking options:
  • http://mi.mathnet.ru/eng/nd712
  • http://mi.mathnet.ru/eng/nd/v16/i2/p309

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Russian Journal of Nonlinear Dynamics
    Number of views:
    This page:39
    Full text:14
    References:4

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021