 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| Klimina L.A., Masterova A.A., Samsonov V.A., and Selyutskiy Yu.D., "Numerical-analytical method for searching for the autorotations of a mechanical system with two rotational degrees of freedom," Mech. Solids. 56 (3), 392-403 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
3 |
Pages |
392-403 |
| DOI |
10.3103/S0025654421030055 |
| Title |
Numerical-analytical method for searching for the autorotations of a mechanical system with two rotational degrees of freedom |
| Author(s) |
Klimina L.A. (Institute of Mechanics, Lomonosov Moscow State University, Moscow, 119192 Russia, klimina@imec.msu.ru)
Masterova A.A. (Institute of Mechanics, Lomonosov Moscow State University, Moscow, 119192 Russia)
Samsonov V.A. (Institute of Mechanics, Lomonosov Moscow State University, Moscow, 119192 Russia)
Selyutskiy Yu.D. (Institute of Mechanics, Lomonosov Moscow State University, Moscow, 119192 Russia) |
| Abstract |
A mechanical system with two rotational degrees of freedom is considered. The mathematical model is presented in the form of a fourth-order dynamic system. A numerical–analytical iterative method is proposed for finding solutions close to periodic, corresponding to the autorotation modes of a mechanical system. Fixed points (including saddles) of the system averaged over two angles are used as a zero approximation. At each iteration, periodic solutions of two auxiliary subsystems are numerically constructed using an approach akin to the Andronov-Pontryagin method. Under the condition of the convergence of the method, a set of periodic functions is obtained, which presumably approximately describe trajectories close to periodic, in particular, quasiperiodic. The conditions for the applicability of the approach are discussed. The proposed method is illustrated by the example of finding the autorotation modes of two interacting Savonius rotors. |
| Keywords |
averaging over two angles, Andronov-Pontryagin method, numerical-analytical method, quasiperiodic solution, autorotation, body in a medium flow |
| Received |
20 May 2020 | Revised |
14 June 2020 | Accepted |
03 July 2020 |
| Link to Fulltext |
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