 | | 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: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
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| In English (Mech. Solids): | | 4811 |
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| S. A. Agafonov and V. A. Matveev, "On the influence of the base vibration on the natural frequencies of a tuned rotor gyroscope," Mech. Solids. 36 (3), 2-6 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
3 |
Pages |
2-6 |
| Title |
On the influence of the base vibration on the natural frequencies of a tuned rotor gyroscope |
| Author(s) |
S. A. Agafonov (Moscow)
V. A. Matveev (Moscow) |
| Abstract |
A one-ring tuned rotor gyroscope (TRG) placed on a
moving base is considered. The base vibrates in accordance with a
fairly generic law described, for example, by quasiperiodic
functions.
Within the framework of the linear model, the motion of a TRG is
governed by a system of differential equations with variable
coefficients. This nonautonomous system of equations is reduced to
an autonomous one with a prescribed accuracy by using a linear
transformation [1]. For the latter system, we use
the Rayleigh theorem generalized to gyroscopic systems [2] to analyze the
evolution of the natural frequencies due to the base vibration.
The particular case where the base vibrates in accordance with a harmonic law
was considered in [3]. The authors of that study analyzed the
role of such vibration in the appearance of errors. Errors of TRG
caused by various sources, including vibrational loads, were
analyzed in detail in [4]. |
| References |
| 1. | S. A. Agafonov, "Stabilization of motion of
nonconservative systems by parametric excitation," Izv. AN. MTT
[Mechanics of Solids], No. 2, pp. 199-202, 1998. |
| 2. | V. F. Zhuravlev, "The Rayleigh theorem generalized
to gyroscopic systems," PMM [Applied Mathematics and
Mechanics], Vol. 40, No. 4, pp. 606-610, 1976. |
| 3. | A. V. Zbrutskii and M. A. Pavlovskii, "Tuned rotor
gyroscope in the conditions of three-dimensional motion of the
base," Izv. AN SSSR. MTT
[Mechanics of Solids], No. 1, pp. 16-26, 1981. |
| 4. | D. S. Pel'por, V. A. Matveev, and V. D. Arseniev, Tuned
Rotor Gyroscopes. Theory and Design [in Russian],
Mashinostroenie, Moscow, 1988. |
| 5. | C. Simó, "Averaging under fast quasi-periodic forcing,"
in Hamiltonian Mechanics: Integrability and Chaotic Behavior. NATO
ASI Series B: Physics., pp. 13-34, Plenum Press, New York, 1994. |
| 6. | B. P. Demidovich, Lectures on Mathematical Theory of
Stability [in Russian], Nauka, Moscow, 1967. |
|
| Received |
15 January 1999 |
| << Previous article | Volume 36, Issue 3 / 2001 | Next article >> |
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