The self-propulsion of a foil with a sharp edge in a viscous fluid under the action of a periodically oscillating rotor. (English) Zbl 1412.37077

Summary: 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.


37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76D09 Viscous-inviscid interaction
70K50 Bifurcations and instability for nonlinear problems in mechanics
Full Text: DOI


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