The Self-propulsion of a Foil with a Sharp Edge in a Viscous Fluid Under the Action of a Periodically Oscillating Rotor
- 3 Downloads
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.
Keywordsself-propulsion Zhukovskii foil foil with a sharp edge motion in a viscous fluid controlled motion period-doubling bifurcation
MSC2010 numbers37Mxx 70Exx 76Dxx
Unable to display preview. Download preview PDF.
- 2.Korotkin A. I. Added Masses of Ship Structures, Fluid Mech. Appl., vol. 88, Dordrecht: Springer, 2009.Google Scholar
- 6.Borisov, A.V., Mamaev, I. S., and Vetchanin, E.V., Self-Propulsion of a Smooth Body in a Viscous Fluid under the Action of a Periodically Oscillating Rotor and Circulation, Regul. Chaotic Dyn., 2018, vol. 23, nos. 7–8, pp. 850–874.Google Scholar
- 8.Mason, R. J., Fluid Locomotion and Trajectory Planning for Shape-Changing Robots, PhD Dissertation, Pasadena,Calif.: California Institute of Technology, 2003, 264 pp.Google Scholar
- 10.Kutta, W.M., Auftriebskräfte in strömenden Flüssigkeiten, Illustr. aeronaut. Mitteilungen, 1902, vol. 6, pp. 133–135.Google Scholar
- 11.Chaplygin, S.A., On the Action of a Plane-Parallel Air Flow upon a Cylindrical Wing Moving within It, in The Selected Works on Wing Theory of Sergei A. Chaplygin, San Francisco: Garbell Research Foundation, 1956, pp. 42–72.Google Scholar
- 18.Tallapragada, Ph., A Swimming Robot with an Internal Rotor As a Nonholonomic System, in Proc. of the American Control Conference (Chicago, Ill., USA, July 1–3, 2015), pp. 657–662.Google Scholar
- 20.Woolsey, C. A. and Leonard, N.E., Underwater Vehicle Stabilization by Internal Rotors, in Proc. of the American Control Conference (San Diego, Calif., 1999), pp. 3417–3421.Google Scholar