 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 50, Issue 6 / 2015 | Next article >> |
| V.P. Ol'shanskii and S.V. Ol'shanskii, "WKB Method for Analyzing the Vibrations of a Meshcherskii Pendulum," Mech. Solids. 50 (6), 615-621 (2015) |
| Year |
2015 |
Volume |
50 |
Number |
6 |
Pages |
615-621 |
| DOI |
10.3103/S0025654415060023 |
| Title |
WKB Method for Analyzing the Vibrations of a Meshcherskii Pendulum |
| Author(s) |
V.P. Ol'shanskii (Petro Vasilenko Kharkiv National Technical University of Agriculture, ul. Artema 44, Kharkiv, 61002 Ukraine)
S.V. Ol'shanskii (National Technical University "Kharkiv Polytechnical Institute," ul. Frunze 21, Kharkiv, 61002, Ukraine, stasolsh77@gmail.com) |
| Abstract |
The WKB method is used to construct an approximate analytic solution of the equation of small nonstationary vibrations of the Meshcherskii mathematical pendulum. The versions of linear and nonlinear variation in the pendulum mass are considered. Calculations showed that, under certain restrictions on the pendulum parameters, the approximate solutions constructed in elementary functions are a good approximation to the exact results. |
| Keywords |
Meshcherskii pendulum, variable mass, WKB method |
| References |
| 1. | I. V. Meshcherskii,
Works on the Mechanics of Bodies of Variable Mass
(Gostekhizdat, Moscow, 1952)
[in Russian]. |
| 2. | V. A. Svetlitskii,
Problems and Examples in the Theory of Oscillations
(Izd-vo MGTU, Moscow, 1994)
[in Russian]. |
| 3. | L. Cveticanin,
Dynamics of Machines with Variable Mass
(Gordon and Brendon, 1998). |
| 4. | S. V. Olshanskii and V. P. Olshanskii,
"Modeling of Vibrations of Oscillator of Variable Mass under Pulse Loading,"
Vestnik NTU "KhPI": Mat. Mod. Tekhn. Tekhnol.,
No. 37 (1010), 125-130 (2013). |
| 5. | E. G. Goloskokov and A. P. Fillipov,
Nonstationary Oscillations of Deformable Systems
(Naukova Dumka, Kiev, 1966)
[in Russian]. |
| 6. | V. P. Olshanskii and S. V. Olshanskii,
"Free Oscillations of Oscillator of Variable Mass,"
Vibr. Tekh. Tekhnol. Vseukr. Nauch.-Tekh. Zh.
No. 2(70), 57-59 (2013). |
| 7. | Yu. A. Mitropolskii,
Nonstationary Processes in Nonlinear Oscillatory Systems
(Izd-vo AN USSR, Kiev, 1955)
[in Russian]. |
| 8. | N. N. Bogolyubov and Yu. A. Mitropolskii,
Asymptotic Methods in Theory of Nonlinear Oscillations
(Nauka, Moscow, 1974)
[in Russian]. |
| 9. | A. P. Bessonov,
Foundations of Dynamics of Mechanisms with Links of Variable Mass
(Nauka, Moscow, 1967)
[in Russian]. |
| 10. | E. Kamke,
Handbook on Ordinary Differential Equations
(Nauka, Moscow, 1976)
[in Russian]. |
| 11. | I. F. Obraztsov, B. V. Nerubailo, and I. V. Andrianov,
Asymptotic Methods in Mechanics of Thin-Wall Structures
(Mashinostroenie, Moscow, 1992) [in Russian]. |
| 12. | L. N. Tishchenko, V. P. Olshanskii, and S. V. Olshanskii,
Vibrations of Grain Flows on Vibration Sieves
(Mis'kdruk, Kharkov, 2012). |
|
| Received |
22 August 2013 |
| Link to Fulltext |
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