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 Regul. Chaotic Dyn., 2018, Volume 23, Issue 7-8, Pages 875–886 (Mi rcd372)

The Self-propulsion of a Foil with a Sharp Edge in a Viscous Fluid Under the Action of a Periodically Oscillating Rotor

Ivan S. Mamaev, Evgeny V. Vetchanin

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: This paper addresses the problem of controlled motion of the Zhukovskii foil in a viscous fluid due to a periodically oscillating rotor. Equations of motion including the added mass effect, viscous friction and lift force due to circulation are derived. It is shown that only limit cycles corresponding to the direct motion or motion near a circle appear in the system at the standard parameter values. The chart of dynamical regimes, the chart of the largest Lyapunov exponent and a one-parameter bifurcation diagram are calculated. It is shown that strange attractors appear in the system due to a cascade of period-doubling bifurcations.

Keywords: self-propulsion, Zhukovskii foil, foil with a sharp edge, motion in a viscous fluid, controlled motion, period-doubling bifurcation

 Funding Agency Grant Number Russian Science Foundation 14-50-00005 This work was supported by the Russian Science Foundation under grant 14-50-00005 and was performed at the Steklov Mathematical Institute of the Russian Academy of Sciences.

DOI: https://doi.org/10.1134/S1560354718070055

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MSC: 37Mxx, 70Exx, 76Dxx
Accepted:26.11.2018
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Citation: 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

Citation in format AMSBIB
\Bibitem{MamVet18} \by Ivan S. Mamaev, Evgeny V. Vetchanin \paper The Self-propulsion of a Foil with a Sharp Edge in a Viscous Fluid Under the Action of a Periodically Oscillating Rotor \jour Regul. Chaotic Dyn. \yr 2018 \vol 23 \issue 7-8 \pages 875--886 \mathnet{http://mi.mathnet.ru/rcd372} \crossref{https://doi.org/10.1134/S1560354718070055} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3910171} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000458183900005} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85061288455} 

• http://mi.mathnet.ru/eng/rcd372
• http://mi.mathnet.ru/eng/rcd/v23/i7/p875

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

This publication is cited in the following articles:
1. A. G. Petrov, “Saturation-Free Numerical Scheme for Computing the Flow Past a Lattice of Airfoils with a Sharp Edge”, Rus. J. Nonlin. Dyn., 15:2 (2019), 135–143
2. E. V. Vetchanin, E. A. Mikishanina, “Vibrational Stability of Periodic Solutions of the Liouville Equations”, Rus. J. Nonlin. Dyn., 15:3 (2019), 351–363
3. 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
4. E. M. Artemova, E. V. Vetchanin, “Control of the motion of a circular cylinder in an ideal fluid using a source”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:4 (2020), 604–617
5. 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