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IssuesArchive of Issues2002-6pp.134-143

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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 7 May 2001
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