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IssuesArchive of Issues2008-2pp.205-217

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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
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