Abstract
The nonlinear effects of a vibrating micromechanical gyroscope with a ring resonator supported by a flexible torsion system are considered. A mathematical model of the thin elastic resonator forced oscillations is derived to account for the nonlinear properties of the resonator material. The resonator dynamics in slow variables measured by the device electronic circuit is investigated according to the Krylov-Bogolyubov averaging method. It is shown that the nonlinear elastic properties of the resonator material led to additional errors of the gyroscope, unstable branches of resonance curves, and quenching.
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Bryan, G.H., On the Beats in the Vibrations of a Revolving Cylinder or Bell//Proc. Camb. Phil. Soc. Math. Phys Sci 1890 V.7 P. 101–111.
Zhuravlev, V.F., About dynamic effects in the elastic rolling ring / Zhuravlev V.F., Klimov D.M. // Izv. AN USSR MTT — 1983. -15. -p. 17–24 (in Russian)
Zhuravlev, VF., Wave solid-state gyroscope / Zhuravlev V.F., Klimov D.M. // Moscow, Nauka, 1985. p. 125 (in Russian)
Zhuravlev, V.F., Theoretical foundations of the wave solid-state gyroscope (VTG)//Izv. RAN MTT —1993, -13, p. 15–26. (in Russian)
Putty M.W., Najali K., A micromachined vibrating ring gyroscope // Proc. Digest, Solid-State Sensors and Actuators Workshop Hilton Head, SC 1994 p. 213–220.
Ayazi, F., Najafi, K., A HARPS S Polysilicon vibrating ring gyroscope // Journal of Micro Electro Mechanical System, V.10 No. 2, 2001, p. 169–179.
Egarmin, N.E., Nonlinear effects in the dynamics of a rotating circular ring // Izv. AN URSS. MTT. -1993, /13, p. 50–59 (in Russian)
Martynenko, Yu.G., Control of nonlinear oscillations of a vibrating ring gyroscope/Martynenko, Yu.G.,Mercuriev, I.V., Podalkov, V.V. // Izv. RAN MTT, -2008-13-p. 77–89 (in Russian).
Krauderer G., Nonlinear mechanic//Moscow, Izd-vo inostr. Lit, 1961.
Filin, A.P., Elements of shells’ theory/Leningrad, Stroiizdat, 1987 (in Russian).
Strett, Jg.V. (lord Relay) Theory of sound. T. 1, Moscow, GITTL, 1955.
Bogolyubov, N.N.., Asymptotic methods in the theory of nonlinear oscillations / Bogolyubov, N.N.., Mitropolskiy, Yu. A. // Moscow, Nauka, 1974. (in Russian)
Zhuravlev, V.F., On the global evolution of the generalized Foucault pendulum // Izv. AN MTT — 1998, 16, p. 5–11. (in Russian)
Zhuravlev, V.F., Driven Foucault pendulum as a model of a class of free gyroscopes // Izv RAN MTT — 1997 -16, p. 27–35.
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Original Russian Text © Yu.G. Martynenko, I. V. Merkuriev, V. V. Podalkov, 2009, published in Giroskopiya i Navigatsiya, 2009, No. 3, pp. 10–22.
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Martynenko, Y.G., Merkuriev, I.V. & Podalkov, V.V. Dynamics of a ring micromechanical gyroscope in the forced-oscillation mode. Gyroscopy Navig. 1, 43–51 (2010). https://doi.org/10.1134/S2075108710010074
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DOI: https://doi.org/10.1134/S2075108710010074