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.
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.
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
\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
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Linking options:
https://www.mathnet.ru/eng/rcd372
https://www.mathnet.ru/eng/rcd/v23/i7/p875
This publication is cited in the following 10 articles:
A. V. Klekovkin, Yu. L. Karavaev, A. A. Kilin, A. V. Nazarov, “Vliyanie khvostovykh plavnikov na skorost vodnogo robota, privodimogo v dvizhenie vnutrennimi podvizhnymi massami”, Kompyuternye issledovaniya i modelirovanie, 16:4 (2024), 869–882
L.A. Klimina, S.A. Golovanov, M.Z. Dosaev, Y.D. Selyutskiy, A.P. Holub, “Plane-parallel motion of a trimaran capsubot controlled with an internal flywheel”, International Journal of Non-Linear Mechanics, 150 (2023), 104341
Yury L. Karavaev, Anton V. Klekovkin, Ivan S. Mamaev, Valentin A. Tenenev, Evgeny V. Vetchanin, “A Simple Physical Model for Control of a Propellerless Aquatic Robot”, Journal of Mechanisms and Robotics, 14:1 (2022)
I. S. Mamaev, I. A. Bizyaev, “Dynamics of an unbalanced circular foil and point vortices in an ideal fluid”, Phys. Fluids, 33:8 (2021), 087119
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
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
Anton V. Klekovkin, Yury L. Karavaev, Ivan S. Mamaev, Evgeny V. Vetchanin, Valentin A. Tenenev, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 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
E. V. Vetchanin, E. A. Mikishanina, “Vibrational Stability of Periodic Solutions of the Liouville Equations”, Rus. J. Nonlin. Dyn., 15:3 (2019), 351–363
A. V. 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
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