 | | 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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| << Previous article | Volume 40, Issue 4 / 2005 | Next article >> |
| V. N. Voronkov, "A method for solving eigenvalue problems for complex linear systems," Mech. Solids. 40 (4), 141-148 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
4 |
Pages |
141-148 |
| Title |
A method for solving eigenvalue problems for complex linear systems |
| Author(s) |
V. N. Voronkov (Korolev) |
| Abstract |
The natural vibrations of a complex system whose subsystems interact at
finitely many points are considered. We assume that the system and its
subsystems are described by ordinary self-adjoint linear differential
operators with discrete spectrum. The couplings between subsystems are
specified by linear homogeneous differential relations.
We solve the problem of synthesizing the natural frequencies and vibration
modes of the system on the basis of given eigenfunctions of the subsystems.
An efficient numerical-analytical method is suggested in which the solution
is sought in the form of series in the eigenfunctions of the subsystems. To
take into account the influence of local couplings between the subsystems,
we introduce correction functions; this permits one to obtain the solution
in the form of rapidly converging series. The method is intended for
determining the natural dynamic characteristics of spacecraft structures. A
sample analysis of a model of such a structure is given. |
| References |
| 1. | V. L. Azarov, L. N. Lupichev, and G. A. Tavrizov, Mathematical
Methods for Complex Systems: Linear Systems [in Russian], Nauka, Moscow,
1975. |
| 2. | L. D. Akulenko and S. V. Nesterov, "On the oscillations of
interacting systems with nonuniform distributed parameters," Izv. AN. MTT
[Mechanics of Solids], No. 2, pp. 15-25, 1999. |
| 3. | A. N. Krylov, Some Differential Equations of Mathematical
Physics [in Russian], Gostekhizdat, Leningrad, 1932. |
| 4. | L. V. Kantorovich, "On general methods of convergence acceleration
in the approximate solution of boundary value problems of mathematical
physics," Trudy In-ta Prom. Stroit., No. 2, pp. 65-72, 1934. |
| 5. | V. N. Voronkov and V. P. Shmakov, "On the representation of
dynamic characteristics of an elastically supported beam via the
characteristics of the free beam," in: Vibrations of Elastic Structures
with Fluid [in Russian], TsNTI "Volna," Moscow, pp. 67-72, 1980. |
| 6. | V. P. Shmakov, "The construction of correction functions in the
Bubnov-Galerkin method," Izv. AN SSSR. MTT [Mechanics of Solids], No. 2,
pp. 80-92, 1981. |
| 7. | A. I. Likhoded, "On the convergence of the method of expansion in
natural vibration modes in dynamic loading problems," Izv. AN SSSR. MTT
[Mechanics of Solids], No. 1, pp. 180-188, 1996. |
| 8. | V. N. Voronkov, "A method for computing heat propagation in a
system of bodies with possible heat exchange,"` in: Actual Problems of
Microelectronics [in Russian], No. 1, TRTI, Taganrog, pp. 127-133, 1990. |
| 9. | M. A. Naimark, Linear Differential Operators [in Russian], Nauka,
Moscow, 1969. |
|
| Received |
29 May 2003 |
| << Previous article | Volume 40, Issue 4 / 2005 | Next article >> |
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