 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 48, Issue 4 / 2013 | Next article >> |
| P.O. Bulanchuk and A.G. Petrov, "Suspension Point Vibration Parameters for a Given Equilibrium of a Double Mathematical Pendulum," Mech. Solids. 48 (4), 380-387 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
4 |
Pages |
380-387 |
| DOI |
10.3103/S0025654413040043 |
| Title |
Suspension Point Vibration Parameters for a Given Equilibrium of a Double Mathematical Pendulum |
| Author(s) |
P.O. Bulanchuk (Institute of Solid State Physics, Russian Academy of Sciences, Akad. Osip'yana 2, Chernogolovka, Moscow oblast, 142432 Russia, bullpav@yandex.ru)
A.G. Petrov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, petrovipmech@gmail.com) |
| Abstract |
The motion of a double mathematical pendulum under the action of the gravity force and a vibration force whose frequency substantially exceeds the system natural frequencies is considered. An oblique vibration stabilizing the pendulum in an arbitrarily given position is sought. The domain of existence of the pendulum equilibrium points and the vibration parameters corresponding to a given equilibrium of the pendulum are obtained analytically. In the domain of existence of equilibrium points, the subdomain of their stability is distinguished. |
| Keywords |
double mathematical pendulum, high-frequency vibration of suspension point, stability |
| References |
| 1. | P. O. Bulanchuk and A. G. Petrov, "Vibrational Energy and Control
of Pendulum Systems," Prikl. Mat. Mekh. 76 (4), 550-562
(2012) [J. Appl. Math. Mech. (Engl. Transl.) 76 (4),
396-404 (2012)]. |
| 2. | A. Stephenson,
"On Induced Stability,"
Phil. Mag. Ser. 7
17, 765-766 (1909). |
| 3. | O. V. Kholostova,
"On Stability of Relative Equilibria of a Double Pendulum with Vibrating Suspension Point,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 4, 18-30 (2011)
[Mech. Solids (Engl. Transl.)
46 (4), 508-518 (2011)]. |
| 4. | E. A. Vishenkova and O. V. Kholostova,
"To Dynamics of a Double Pendulum with a Horizontally Vibrating Point of Suspension,"
Vestnik Udmurt. Univ. Mat. Mekh. Komp. Nauki.,
No. 2, 114-129 (2012). |
| 5. | T. G. Strizhak,
Averaging Methods in Problems of Mechanics
(Vishcha Shkola, Kiev-Donetsk, 1982)
[in Russian]. |
| 6. | P. O. Bulanchuk and A. G. Petrov,
"Control of the Equilibrium Point of Simple and Double Mathematical Pendulums with Oblique Vibration,"
Dokl. Ross. Akad. Nauk
442 (4), 474-378 (2012)
[Dokl. Phys. (Engl. Transl.)
57 (2), 73-77 (2012)]. |
| 7. | A. G. Petrov,
"Vibratory Energy of a Conservative Mechanical System,"
Dokl. Ross. Akad. Nauk
431 (6), 762-765 (2010)
[Dokl. Phys. (Engl. Transl.)
55 (4), 203-206 (2010)]. |
| 8. | N. N. Bogolyubov and Yu. A. Mitropol'skii,
Asymptotic Methods in Theory of Nonlinear Oscillations
(Nauka, Moscow, 1974)
[in Russian]. |
| 9. | V. Ph. Zhuravlev and D. M. Klimov,
Applied Methods in the Theory of Vibrations
(Nauka, Moscow, 1988)
[in Russian]. |
|
| Received |
01 March 2013 |
| Link to Fulltext |
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