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
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.
self-propulsion, Zhukovskii foil, foil with a sharp edge, motion in a viscous fluid, controlled motion, period-doubling bifurcation
|Russian Science Foundation
|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.
MSC: 37Mxx, 70Exx, 76Dxx
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
\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.
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