 | | 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
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| In English (Mech. Solids): | | 4760 |
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| A. O. Belyakov and A. P. Seiranyan, "Determining the moments of inertia of large bodies from vibrations in elastic suspension," Mech. Solids. 43 (2), 205-217 (2008) |
| Year |
2008 |
Volume |
43 |
Number |
2 |
Pages |
205-217 |
| DOI |
10.3103/S0025654408020052 |
| Title |
Determining the moments of inertia of large bodies from vibrations in elastic suspension |
| Author(s) |
A. O. Belyakov (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192, Russia, a_belyakov@inbox.ru)
A. P. Seiranyan (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192, Russia, seyran@imec.msu.ru) |
| Abstract |
To ensure the maneuvering capabilities of aircraft and high-speed sea vessels, designers should know the moments of inertia of their massive parts. But since the structure of some elements such as power units is very complicated, it is impossible to determine their moments of inertia analytically. Thus the problem of measuring the moments of inertia of massive large bodies arises. To this end, a measuring bench was designed in N. E. Zhukovskii Central Institute for Aerohydrodynamics (TsAGI) on the basis of a new method for determining the body moments of inertia from vibrations in the elastic suspension [1]. In this connection, it is necessary to develop the corresponding mathematical algorithms for determining the moments of inertia.
In this paper, we develop mathematical algorithms for determining the body moments of inertia by using methods for identification of linear systems in the state space [2-5]. We present three versions of solving the problem of determining the body moments of inertia depending on the information about the method for exciting the vibrations or about the body parameters and the rigidity of the bench springs. We study the influence of damping on the accuracy of determining the moments of inertia. Numerical results are given for a specific system. |
| References |
| 1. | V. V. Bogdanov, V. S. Volobuev, A. I. Kudryashov, and V. V. Travin,
"A Suite for Measuring Mass, Coordinates of the Center of Mass,
and Moments of Inertia of Engineering Components,"
Izmer. Tekh.,
No. 2, 37-39 (2002)
[Measurement Techniques (Engl. Transl.)
45 (2), 168-172 (2002)]. |
| 2. | S. Y. Kung,
"A New Identification and Model Reduction Algorithm
via Singular Value Decomposition,"
in Paper 12th Asilomar Conf. Circuits, Syst. Comput.
(Pacific Grove, Calf., 1978). |
| 3. | A. O. Belyakov and L. Yu. Blazhennova-Mikulich,
"Identification of Inertia Matrix of Conservative Oscillatory
System,"
Vestnik Moskov. Univ. Ser. I. Mat. Mekh.,
No. 3, 25-28 (2005)
[Moscow Univ. Math. Bull. (Engl. Transl.)] |
| 4. | M. Verhaegen,
"Identification of the Deterministic Part of MIMO State Space Models
Given in Innovation Forms from Input-Output Data,"
Automatica
30 (1), 61-74 (1994). |
| 5. | M. Viberg, "Subspace-Based Methods for the Identification of
Linear Time-Invariant Systems," Automatica 31 (12),
1835-1851 (1995). |
| 6. | A. P. Markeev,
Theoretical Mechanics
(Nauka, Moscow, 1990)
[in Russian]. |
| 7. | I. V. Novozhilov,
Fractional Analysis
(Izd-vo MGU, Moscow, 1995)
[in Russian]. |
| 8. | Yu. A. Amenzade,
Theory of Elasticity
(Vysshaya Shkola, Moscow, 1976)
[in Russian]. |
| 9. | A. Yu. Ishlinskii,
Mechanics of Gyroscopic Systems
(Izd. AN SSSR, Moscow, 1963)
[in Russian]. |
| 10. | A. O. Belyakov, "Determination of Dynamic Parameters of Massive
Bodies by Vibration Modes," Vestnik Molodykh Uchenykh. Ser. Prikl.
Mat. Mekh., St-Petersburg, No. 12, 33-36 (2003). |
| 11. | V. F. Zhuravlev and D. M. Klimov, Applied Methods in the
Theory of Vibrations (Nauka, Moscow, 1983) [in Russian]. |
| 12. | M. I. Vishik and L. A. Lyusternik,
"The Solution of Some Perturbation Problems for Matrices and
Selfadjoint or Non-Selfadjoint Differential Equations I,"
Uspekhi Mat. Nauk
15 (3), 3-80 (1960)
[Russ. Math. Surv. (Engl. Transl.)
15 (3), 1-73 (1960)]. |
| 13. | A. P. Seyranian and A. A. Mailybaev,
Multiparameter Stability Theory with Mechanical Applications
(World Scientific, Singapore, 2003). |
| 14. | F. R. Gantmakher,
Theory of Matrices
(Nauka, Moscow, 1988)
[in Russian]. |
| 15. | F. R. Gantmakher,
Lectures on Analytical Mechanics
(Nauka, Moscow, 1966; Chelsea, New York, 1970). |
| 16. | A. O. Belyakov, "Numerical Modeling of Measurement Process of
Inertia Moments of Large Bodies by Free Vibration Method," Uchen.
Zapiski TsAGI, No. 1-2, 129-136 (2002). |
|
| Received |
15 September 2005 |
| Link to Fulltext |
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