Abstract:
This article is devoted to the study of self-propulsion of bodies in a fluid by the action of internal mechanisms, without changing the external shape of the body. The paper presents an overview of theoretical papers that justify the possibility of this displacement in ideal and viscous liquids.
A special case of self-propulsion of a rigid body along the surface of a liquid is considered due to the motion of two internal masses along the circles. The paper presents a mathematical model of the motion of a solid body with moving internal masses in a three-dimensional formulation. This model takes into account the three-dimensional vibrations of the body during motion, which arise under the action of external forces-gravity force, Archimedes force and forces acting on the body, from the side of a viscous fluid.
The body is a homogeneous elliptical cylinder with a keel located along the larger diagonal. Inside the cylinder there are two material point masses moving along the circles. The centers of the circles lie on the smallest diagonal of the ellipse at an equal distance from the center of mass.
Equations of motion of the system (a body with two material points, placed in a fluid) are represented as Kirchhoff equations with the addition of external forces and moments acting on the body. The phenomenological model of viscous friction is quadratic in velocity used to describe the forces of resistance to motion in a fluid.The coefficients of resistance to movement were determined experimentally. The forces acting on the keel were determined by numerical modeling of the keel oscillations in a viscous liquid using the Navier–Stokes equations.
In this paper, an experimental verification of the proposed mathematical model was carried out. Several series of experiments on self-propulsion of a body in a liquid by means of rotation of internal masses with different speeds of rotation are presented. The dependence of the average propagation velocity, the amplitude of the transverse oscillations as a function of the rotational speed of internal masses is investigated. The obtained experimental data are compared with the results obtained within the framework of the proposed mathematical model.
Keywords:
motion in a fluid, self-promotion, the equations of movement, above-water screwless robot, Navier–Stokes equations.
The work of A. A. Kilin was supported by the Russian Foundation for Basic Research under grant No. 15-08-09093-а. The
work of A. I. Klenov and V. A. Tenenev carried out within the framework of the state assignment by the Ministry of Education
and Science No. 1.2405.2017/4.6.
Received: 06.04.2018 Accepted: 04.05.2018
Document Type:
Article
UDC:519.8
Language: Russian
Citation:
A. A. Kilin, A. I. Klenov, V. A. Tenenev, “Controlling the movement of the body using internal masses in a viscous liquid”, Computer Research and Modeling, 10:4 (2018), 445–460
\Bibitem{KilKleTen18}
\by A.~A.~Kilin, A.~I.~Klenov, V.~A.~Tenenev
\paper Controlling the movement of the body using internal masses in a viscous liquid
\jour Computer Research and Modeling
\yr 2018
\vol 10
\issue 4
\pages 445--460
\mathnet{http://mi.mathnet.ru/crm457}
\crossref{https://doi.org/10.20537/2076-7633-2018-10-4-445-460}
Linking options:
https://www.mathnet.ru/eng/crm457
https://www.mathnet.ru/eng/crm/v10/i4/p445
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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
M. A. Garbuz, M. Z. Dosaev, V. A. Samsonov, “ORGANIZATsIYa POVOROTA KORPUSA VIBRATsIONNOGO ROBOTA VOKRUG VERTIKALI”, Izvestiya Rossiiskoi akademii nauk. Teoriya i sistemy upravleniya, 2023, no. 1, 164
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)
Sergey Golovanov, Liubov Klimina, Marat Dosaev, Yury Selyutskiy, Andrei Holub, 2022 16th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), 2022, 1
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