This article is cited in 4 scientific papers (total in 4 papers)
Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation
Alexey V. Borisova, Ivan S. Mamaevba, Eugeny V. Vetchaninab
a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia
This paper addresses the problem of self-propulsion of a smooth profile in a medium with viscous dissipation and circulation by means of parametric excitation generated by oscillations of the moving internal mass. For the case of zero dissipation, using methods of KAM theory, it is shown that the kinetic energy of the system is a bounded function of time, and in the case of nonzero circulation the trajectories of the profile lie in a bounded region of the space. In the general case, using charts of dynamical regimes and charts of Lyapunov exponents, it is shown that the system can exhibit limit cycles (in particular, multistability), quasi-periodic regimes (attracting tori) and strange attractors. One-parameter bifurcation diagrams are constructed, and Neimark – Sacker bifurcations and period-doubling bifurcations are found. To analyze the efficiency of displacement of the profile depending on the circulation and parameters defining the motion of the internal mass, charts of values of displacement for a fixed number of periods are plotted. A hypothesis is formulated that, when nonzero circulation arises, the trajectories of the profile are compact. Using computer calculations, it is shown that in the case of anisotropic dissipation an unbounded growth of the kinetic energy of the system (Fermi-like acceleration) is possible.
self-propulsion in a fluid, motion with speed-up, parametric excitation, viscous dissipation, circulation, period-doubling bifurcation, Neimark – Sacker bifurcation, Poincaré map, chart of dynamical regimes, chart of Lyapunov exponents, strange att
|Ministry of Education and Science of the Russian Federation
|Russian Foundation for Basic Research
|The work of A.V. Borisov (Introduction and Section 1) was carried out within the framework of the state assignment to the Udmurt State University 1.2404.2017/4.6. The work of E.V. Vetchanin and I. S.Mamaev (Sections 2 and 3) was carried out within the framework of the state assignment to the Izhevsk State Technical University 1.2405.2017/4.6 and was supported by the RFBR grant No 15-08-09093-a.
MSC: 70H08, 70Exx, 76Bxx, 76Dxx
Alexey V. Borisov, Ivan S. Mamaev, Eugeny V. Vetchanin, “Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation”, Regul. Chaotic Dyn., 23:4 (2018), 480–502
Citation in format AMSBIB
\by Alexey V. Borisov, Ivan S. Mamaev, Eugeny V. Vetchanin
\paper Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation
\jour Regul. Chaotic Dyn.
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Alexey V. Borisov, Ivan S. Mamaev, Evgeny V. Vetchanin, “Self-propulsion of a Smooth Body in a Viscous Fluid Under Periodic Oscillations of a Rotor and Circulation”, Regul. Chaotic Dyn., 23:7-8 (2018), 850–874
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
I. S. Mamaev, V. A. Tenenev, E. V. Vetchanin, “Dynamics of a Body with a Sharp Edge in a Viscous Fluid”, Nelineinaya dinam., 14:4 (2018), 473–494
Kilin A.A. Pivovarova E.N., “Chaplygin TOP With a Periodic Gyrostatic Moment”, Russ. J. Math. Phys., 25:4 (2018), 509–524
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