Geodesic
Dynamics of an $L$-$L$-type two-mass micromechanical gyroscope under forced oscillations
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 74 (2021), pp. 63-70 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper is devoted to a study of dynamics of an $L$-$L$-type two-mass micromechanical gyroscope (abbreviated as MMG) under forced oscillations. The mechanical-theoretical model of MMG with a sensitive element in the form of a model with two active masses (“Inertial mass -Frame”) is obtained. Based on the model, the system of differential equations is written. A distinctive feature of this paper is that an arbitrary angular velocity of the base $\Omega$ is considered. A new method is used to find a solution to the system. This method is suitable for analyzing dualfrequency systems. Finally, the solution is determined, and the amplitude-frequency characteristics of the system are described. The obtained analytical expressions and graphs are analyzed, and the reasonable conclusions about system behavior under forced oscillations are made. The proposed method for analyzing complex systems is compared with other available methods.
Keywords: micromechanical gyroscope, linear vibrations, forced oscillations, linear system. 
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     author = {E. A. Antonov},
     title = {Dynamics of an $L$-$L$-type two-mass micromechanical gyroscope under forced oscillations},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {63--70},
     year = {2021},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2021_74_a6/}
}
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E. A. Antonov. Dynamics of an $L$-$L$-type two-mass micromechanical gyroscope under forced oscillations. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 74 (2021), pp. 63-70. http://geodesic.mathdoc.fr/item/VTGU_2021_74_a6/

[1] Blixhaven B., Lapadatu D., Holm R., Kvisterfy T., “SAR-500-A novel high-precision gyroscope”, Symposium Gyro Technology (Karlsruhe, Germany, 2010)

[2] Peshekhonov V.G., “Sovremennoe sostoyanie i perspektivy razvitiya giroskopicheskikh sistem”, Giroskopiya i navigatsiya, 2011, no. 1, 3–17

[3] Naraikin O.S., Sorokin F.D., Kozubnyak S.A., Vakhlyarskii D.S., “Chislennoe modelirovanie pretsessii uprugoi volny v tsilindricheskom rezonatore volnovogo tverdotelnogo giroskopa s neodnorodnym raspredeleniem plotnosti”, Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie, 2017, no. 5, 41–51 | DOI

[4] Lestev A.M., Efimovskaya A.V., “O vliyanii nelineinykh faktorov na dinamiku mikromekhanicheskogo giroskopa s dvukhmassovym chuvstvitelnym elementom”, Izvestiya vysshikh uchebnykh zavedenii. Priborostroenie, 55:5 (2012), 40–46

[5] Evstifeev M.I., Chelpanov I.B., “Voprosy obespecheniya stoikosti mikromekhanicheskikh giroskopov pri mekhanicheskikh vozdeistviyakh”, Giroskopiya i navigatsiya, 2013, no. 1, 119–131

[6] Burtsev V.A., Dergachev P.B., Karelin A.P., Lestev A.M., Lestev M.A., Popova I.V., Semenov A.A., Mikromekhanicheskoi giroskop, Patent na poleznuyu model RU 30972 U1 MPK G01C 19/56 ot 2003.02.04/Opubl. 2003.07.10

[7] Zhuravlev V.F., “Upravlyaemyi mayatnik Fuko kak model odnogo klassa svobodnykh giroskopov”, Izv. RAN. MTT, 1997, no. 6, 27–35

[8] Bogolyubov N.N., Mitropolskii Yu.A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974, 503 pp. | MR

[9] Naife A., Metody vozmuschenii, Mir, M., 1976, 456 pp.