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Regul. Chaotic Dyn., 2018, том 23, выпуск 4, страницы 480–502 (Mi rcd335)  

Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)

Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation

Alexey V. Borisova, Ivan S. Mamaevba, Eugeny V. Vetchaninab

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia

Аннотация: This paper addresses the problem of self-propulsion of a smooth profile in a medium with viscous dissipation and circulation by means of parametric excitation generated by oscillations of the moving internal mass. For the case of zero dissipation, using methods of KAM theory, it is shown that the kinetic energy of the system is a bounded function of time, and in the case of nonzero circulation the trajectories of the profile lie in a bounded region of the space. In the general case, using charts of dynamical regimes and charts of Lyapunov exponents, it is shown that the system can exhibit limit cycles (in particular, multistability), quasi-periodic regimes (attracting tori) and strange attractors. One-parameter bifurcation diagrams are constructed, and Neimark – Sacker bifurcations and period-doubling bifurcations are found. To analyze the efficiency of displacement of the profile depending on the circulation and parameters defining the motion of the internal mass, charts of values of displacement for a fixed number of periods are plotted. A hypothesis is formulated that, when nonzero circulation arises, the trajectories of the profile are compact. Using computer calculations, it is shown that in the case of anisotropic dissipation an unbounded growth of the kinetic energy of the system (Fermi-like acceleration) is possible.

Ключевые слова: self-propulsion in a fluid, motion with speed-up, parametric excitation, viscous dissipation, circulation, period-doubling bifurcation, Neimark – Sacker bifurcation, Poincaré map, chart of dynamical regimes, chart of Lyapunov exponents, strange att

Финансовая поддержка Номер гранта
Министерство образования и науки Российской Федерации 1.2404.2017/4.6
1.2405.2017/4.6
Российский фонд фундаментальных исследований 15-08-09093-a
The work of A.V. Borisov (Introduction and Section 1) was carried out within the framework of the state assignment to the Udmurt State University 1.2404.2017/4.6. The work of E.V. Vetchanin and I. S.Mamaev (Sections 2 and 3) 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 15-08-09093-a.


DOI: https://doi.org/10.1134/S1560354718040081

Список литературы: PDF файл   HTML файл

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Тип публикации: Статья
MSC: 70H08, 70Exx, 76Bxx, 76Dxx
Поступила в редакцию: 15.05.2018
Принята в печать:19.06.2018
Язык публикации: английский

Образец цитирования: Alexey V. Borisov, Ivan S. Mamaev, Eugeny V. Vetchanin, “Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation”, Regul. Chaotic Dyn., 23:4 (2018), 480–502

Цитирование в формате AMSBIB
\RBibitem{BorMamVet18}
\by Alexey V. Borisov, Ivan S. Mamaev, Eugeny V. Vetchanin
\paper Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 4
\pages 480--502
\mathnet{http://mi.mathnet.ru/rcd335}
\crossref{https://doi.org/10.1134/S1560354718040081}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3836283}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85051117098}


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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. 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  mathnet  crossref
    2. 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
    3. I. S. Mamaev, V. A. Tenenev, E. V. Vetchanin, “Dynamics of a Body with a Sharp Edge in a Viscous Fluid”, Нелинейная динам., 14:4 (2018), 473–494  mathnet  crossref
    4. Kilin A.A. Pivovarova E.N., “Chaplygin TOP With a Periodic Gyrostatic Moment”, Russ. J. Math. Phys., 25:4 (2018), 509–524  crossref  mathscinet  zmath  isi  scopus
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