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Regular and Chaotic Dynamics

, Volume 23, Issue 7–8, pp 875–886 | Cite as

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

  • Ivan S. MamaevEmail author
  • Evgeny V. Vetchanin
Article
  • 3 Downloads

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 

MSC2010 numbers

37Mxx 70Exx 76Dxx 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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