 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| L.D. Akulenko and S.V. Nesterov, "Parametric Vibrations of a Mechanical System and Their Stability for an Arbitrary Modulation Coefficient," Mech. Solids. 48 (2), 119-127 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
2 |
Pages |
119-127 |
| DOI |
10.3103/S0025654413020015 |
| Title |
Parametric Vibrations of a Mechanical System and Their Stability for an Arbitrary Modulation Coefficient |
| Author(s) |
L.D. Akulenko (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, gavrikov@ipmnet.ru)
S.V. Nesterov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia) |
| Abstract |
The natural frequencies and modes of parametric vibrations of a
mechanical system are studied, by way of example, for a pendulum of
variable length with modulation coefficient varying from arbitrarily small to maximum admissible values. Analytic and numerical methods are used to construct and study the boundaries of the resonance domains for the first four vibration modes, and the main qualitative properties of higher modes are found. The complete degeneration of modes with even numbers, i.e., the coincidence of the frequencies of symmetric and nonsymmetric natural modes for admissible values of the modulation parameter, is proved. The global picture of boundaries of stability domains for the lower equilibrium is constructed, and a significant difference from the Ince-Strutt diagram is shown. Specific properties of the natural modes are established. |
| Keywords |
pendulum, variable length, parametric vibrations, modulation coefficient, resonance domain, natural frequency, natural mode |
| References |
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[in Russian]. |
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[in Russian]. |
| 3. | I. G. Malkin,
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| 17. | L. D. Akulenko and S. B. Nesterov,
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Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 56-68 (1998)
[Mech. Solids (Engl. Transl.)
33 (4), 48-58 (1998)]. |
| 18. | L. D. Akulenko and S. B. Nesterov,
High-Precision Methods in Eigenvalue Problems and Their Applications
(CRC Press, Boca Raton, 2005). |
| 19. | L. D. Akulenko and S. B. Nesterov,
"Parametric Oscillations and Stability of Systems with Large Modulation Coefficient,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 62-68 (2008)
[Mech. Solids (Engl. Transl.)
43 (3), 366-371 (2008)]. |
|
| Received |
08 September 2011 |
| Link to Fulltext |
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