Regular and Chaotic Dynamics
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Regul. Chaotic Dyn., 2018, том 23, выпуск 7-8, страницы 850–874 (Mi rcd371)  

Эта публикация цитируется в 9 научных статьях (всего в 9 статьях)

Self-propulsion of a Smooth Body in a Viscous Fluid Under Periodic Oscillations of a Rotor and Circulation

Alexey V. Borisova, Ivan S. Mamaevb, Evgeny V. Vetchaninc

a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
b Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia
c Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

Аннотация: This paper addresses the problem of the self-propulsion of a smooth body in a fluid by periodic oscillations of the internal rotor and circulation. In the case of zero dissipation and constant circulation, it is shown using methods of KAM theory that the kinetic energy of the system is a bounded function of time. In the case of constant nonzero circulation, the trajectories of the center of mass of the system lie in a bounded region of the plane. The method of expansion by a small parameter is used to approximately construct a solution corresponding to directed motion of a circular foil in the presence of dissipation and variable circulation. Analysis of this approximate solution has shown that a speed-up is possible in the system in the presence of variable circulation and in the absence of resistance to translational motion. It is shown that, in the case of an elliptic foil, directed motion is also possible. To explore the dynamics of the system in the general case, bifurcation diagrams, a chart of dynamical regimes and a chart of the largest Lyapunov exponent are plotted. It is shown that the transition to chaos occurs through a cascade of period-doubling bifurcations.

Ключевые слова: self-propulsion in a fluid, smooth body, viscous fluid, periodic oscillation of circulation, control of a rotor

Финансовая поддержка Номер гранта
Российский фонд фундаментальных исследований 18-29-10050 mk
18-08-00995 A
Российский научный фонд 18-71-00111
Министерство образования и науки Российской Федерации 1.2405.2017/4.6
The work of A.V. Borisov was supported by the RFBR grant No. 18-29-10050 mk. The work of E.V. Vetchanin (Sections 3, 4, and 5) was supported by the Russian Science Foundation under grant 18-71-00111. The work of I.S. Mamaev was carried out within the framework of the state assignment to the Izhevsk State Technical University 1.2405.2017/4.6 and was supported by the RFBR grant No 18-08-00995 A.


DOI: https://doi.org/10.1134/S1560354718070043

Список литературы: PDF файл   HTML файл

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Тип публикации: Статья
MSC: 37Mxx, 70Exx, 76Dxx
Поступила в редакцию: 31.10.2018
Принята в печать:03.12.2018
Язык публикации: английский

Образец цитирования: Alexey V. Borisov, Ivan S. Mamaev, Evgeny V. Vetchanin, “Self-propulsion of a Smooth Body in a Viscous Fluid Under Periodic Oscillations of a Rotor and Circulation”, Regul. Chaotic Dyn., 23:7-8 (2018), 850–874

Цитирование в формате AMSBIB
\RBibitem{BorMamVet18}
\by Alexey V. Borisov, Ivan S. Mamaev, Evgeny V. Vetchanin
\paper Self-propulsion of a Smooth Body in a Viscous Fluid Under Periodic Oscillations of a Rotor and Circulation
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 7-8
\pages 850--874
\mathnet{http://mi.mathnet.ru/rcd371}
\crossref{https://doi.org/10.1134/S1560354718070043}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85061296452}


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

    Эта публикация цитируется в следующих статьяx:
    1. Ivan S. Mamaev, Evgeny V. Vetchanin, “The Self-propulsion of a Foil with a Sharp Edge in a Viscous Fluid Under the Action of a Periodically Oscillating Rotor”, Regul. Chaotic Dyn., 23:7-8 (2018), 875–886  mathnet  crossref  mathscinet
    2. E. V. Vetchanin, “The Motion of a Balanced Circular Cylinder in an Ideal Fluid Under the Action of External Periodic Force and Torque”, Rus. J. Nonlin. Dyn., 15:1 (2019), 41–57  mathnet  crossref  elib
    3. L. I. Mogilevich, S. V. Ivanov, “The Study of Wave Propagation in a Shell with Soft Nonlinearity and with a Viscous Liquid Inside”, Rus. J. Nonlin. Dyn., 15:3 (2019), 233–250  mathnet  crossref  mathscinet
    4. E. V. Vetchanin, E. A. Mikishanina, “Vibrational Stability of Periodic Solutions of the Liouville Equations”, Rus. J. Nonlin. Dyn., 15:3 (2019), 351–363  mathnet  crossref  mathscinet
    5. V A. Borisov , E. V. Vetchanin, I. S. Mamaev, “Motion of a smooth foil in a fluid under the action of external periodic forces. I”, Russ. J. Math. Phys., 26:4 (2019), 412–427  crossref  mathscinet  zmath  isi  scopus
    6. L. I. Mogilevich, S. V. Ivanov, Yu. A. Blinkov, “Modeling of Nonlinear Waves in Two Coaxial Physically Nonlinear Shells with a Viscous Incompressible Fluid Between Them, Taking into Account the Inertia of its Motion”, Rus. J. Nonlin. Dyn., 16:2 (2020), 275–290  mathnet  crossref
    7. E. M. Artemova, E. V. Vetchanin, “Control of the motion of a circular cylinder in an ideal fluid using a source”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 30:4 (2020), 604–617  mathnet  crossref
    8. E. V. Vetchanin, I. S. Mamaev, “Asymptotic behavior in the dynamics of a smooth body in an ideal fluid”, Acta Mech., 231:11 (2020), 4529–4535  crossref  mathscinet  zmath  isi  scopus
    9. A. V. Borisov, E. V. Vetchanin, I. S. Mamaev, “Motion of a smooth foil in a fluid under the action of external periodic forces. II”, Russ. J. Math. Phys., 27:1 (2020), 1–17  crossref  mathscinet  zmath  isi  scopus
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