 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| Yu. G. Balakirev, "Convergence acceleration for modal expansions in problems of synthesis of dynamical characteristics of composite structures," Mech. Solids. 37 (6), 134-143 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
6 |
Pages |
134-143 |
| Title |
Convergence acceleration for modal expansions in problems of synthesis of dynamical characteristics of composite structures |
| Author(s) |
Yu. G. Balakirev (Korolev) |
| Abstract |
The classical methods of convergence acceleration for functional series
and their applications to the solution of boundary value problems have been
considered in the well known publications of A. N. Krylov,
L. V. Kantorovich, and A. I. Lur'e [1-3]. A new wave of investigations in
this field is due the following works: [4, 5], where correction functions
are introduced for the investigation of vibration problems for elastic
structures; [6], where methods of convergence acceleration of Green's
functions in problems of steady vibrations of beams are developed; [7],
where multiple identification of quasistatic components is proposed for problems of
dynamic loading of elastic structures, with the irregularity of external
loads taken into account. Convergence acceleration for series
in problems of composite structure design by the method of synthesis
is considered in [8-10]. The present paper is aimed at a critical analysis of
various approaches to the construction of correction functions and their effect on
the convergence of modal expansions in problems of synthesis of the dynamical
characteristics of composite structures by the method of forces. |
| References |
| 1. | A. N. Krylov, Lectures on Approximate Calculations [in Russian],
Gostekhteorizdat, Moscow, Leningrad, 1964. |
| 2. | L. V. Kantorovich and V. I. Krylov,
Approximate Methods of Higher Analysis [in Russian],
Gostekhteorizdat, Moscow, Leningrad, 1949. |
| 3. | A. I. Lur'e, Theory of Elasticity [in Russian], Nauka, Moscow, 1970. |
| 4. | V. P. Shmakov, "On an approach simplifying the application of the
Bubnov-Galerkin method for solving boundary value problems,"
Inzh. Zh. MTT, No. 5, pp. 129-136, 1967. |
| 5. | V. P. Shmakov, "Construction of correcting functions in the
Bubnov-Galerkin method," Izv. AN SSSR. MTT [Mechanics of Solids],
No. 2, pp. 80-92, 1981. |
| 6. | V. L. Azarov, L. N. Lupichev, and G. A. Tavrizov,
Mathematical Methods for the Investigation of Complex Physical Systems [in Russian],
Nauka, Moscow, 1975. |
| 7. | A. I. Likhoded, "On the convergence of the
method of expansion in terms of eigenfunctions in
problems of dynamic loading," Izv. AN SSSR. MTT [Mechanics of Solids],
No. 1, pp. 180-188, 1986. |
| 8. | R. R. Craig and C. C. Bampton,
"Coupling of substructures for dynamic analysis,"
AIAA J., Vol. 6, No. 7, pp. 1313-1319, 1968. |
| 9. | R. R. Craig and C.-J. Chang,
" Free-interface methods of substructure coupling for
dynamic analysis," AIAA J., Vol. 14, No. 11, pp. 1633-1635, 1976. |
| 10. | V. P. Shmakov, "The method of synthesis of
dynamical characteristics of elastic module structures,"
Vestnik MGTU. Ser. Mashinostr., No. 1, pp. 4-10, 1991. |
| 11. | V. G. Grigor'ev,
"On computational aspects of the application of correcting series
for the synthesis of substructures by the method of free boundaries,"
Vestnik MGTU. Ser. Mashinostr., No. 4, pp. 17-27, 1998. |
| 12. | V. P. Shmakov and V. G. Grigor'ev,
"Synthesis of dynamical characteristics of analytic and discrete modules
of substructures by means of correcting series,"
Vestnik MGTU. Ser. Mashinostr., No. 2, pp. 5-19, 2000. |
| 13. | V. P. Shmakov,
"Approximation of harmonic response of an elastic finite-dimensional system
according to the frequency range of external excitations,"
Vestnik MGTU. Ser. Mashinostr., No. 2, pp. 96-110, 1995. |
|
| Received |
07 May 2001 |
| << Previous article | Volume 37, Issue 6 / 2002 | Next article >> |
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