 | | 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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| << Previous article | Volume 46, Issue 2 / 2011 | Next article >> |
| Yu.G. Balakirev, "On Quasistatics and Correcting Functions in the Dynamics of Elastic Structures," Mech. Solids. 46 (2), 230-238 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
2 |
Pages |
230-238 |
| DOI |
10.3103/S0025654411020117 |
| Title |
On Quasistatics and Correcting Functions in the Dynamics of Elastic Structures |
| Author(s) |
Yu.G. Balakirev (Moscow State Technical University "MAMI," Bol'shaya Semyonovskaya 38, Moscow, 107023 Russia, balakirevyug@mail.ru) |
| Abstract |
A new method is proposed for constructing quasistatic terms that are required to refine the solution of the problem of dynamic loading of an elastic structure with energy scattering taken into account and a bounded number of coordinate functions used in the modal expansion. The quasistatic terms introduced are orthogonal to the mode shapes taken into account in the calculations of the vibration harmonics and compensate the quasistatic contribution of the neglected vibration harmonics. The identity between the procedures of introducing correcting functions (correcting series) and refining the quasistatics is discussed. |
| Keywords |
elastic structures, dynamic loading, quasistatics, free vibration, correcting functions |
| References |
| 1. | A. G. Gorshkov, V. I. Morozov, A. T. Ponomarev, and F. N. Shklyarchuk,
Aerohydroelasticity of Structures
(Nauka, Fizmatlit, Moscow, 2000)
[in Russian]. |
| 2. | A. I. Likhoded,
"On the Convergence of the Method of Expansion in Natural Vibration Modes
in Problems of Dynamic Loading,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 1, 180-188 (1986)
[Mech. Solids (Engl. Transl.)]. |
| 3. | V. P. Shmakov,
"On a Method Simplifying the Bubnov-Galerkin Method Application
for Solving Boundary-Value Problems,"
Inzh. Zh. Mekh. Tverd. Tela.
No. 5, 129-136 (1967). |
| 4. | V. P. Shmakov,
"The Construction of Correction Functions in the Bubnov-Galerkin Method,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 2, 80-92 (1981)
[Mech. Solids (Engl. Transl.)]. |
| 5. | V. P. Shmakov,
"Method of Synthesis of Dynamic Characteristics for Elastic Modular Structures,"
Vest. MGTU. Ser. Mashinostr.,
No. 1, 4-10 (1991). |
| 6. | V. P. Shmakov,
"Approximation of the Harmonic Response of an Elastic Finite-Dimensional System
Dependent on the Frequency Range of the External Action,"
Vest. MGTU. Ser. Mashinostr.,
No. 2, 96-110 (1995). |
| 7. | V. G. Grigoriev,
"On Computational Aspects of Applying Correcting Series in the Synthesis
of Substructures by the Free Boundary Method,"
Vest. MGTU, Ser. Mashinostr.,
No. 4, 17-27 (1998). |
| 8. | V. P. Shmakov and V. G. Grigoriev,
"Synthesis of Dynamic Characteristics of Analytical and Discrete Models of Substructures
with the Use of Correcting Series,"
Vest. MGTU, Ser. Mashinostr.,
No. 2, 5-19 (2000). |
| 9. | Yu. G. Balakirev,
"Convergence Acceleration for Modal Expansions in Problems of Synthesis
of Dynamical Characteristics of Composite Structures,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 158-170 (2002)
[Mech. Solids (Engl. Transl.)
37 (6), 134-143 (2002)]. |
| 10. | Yu. G. Balakirev,
"Features of the Construction of Correction Functions in the Analysis of the
Free Vibrations of Mechanical Systems by Bubnov's Method,"
Prikl. Mat. Mekh.
67 (6), 1040-1050 (2003)
[J. Appl. Math. Mech. (Engl. Transl.)
67 (6), 911-920 (2003)]. |
| 11. | Yu. G. Balakirev,
"Additional Possibilities for Using the Bubnov Method
in Studies of Forced Vibration of Elastic Structures,"
in Proc. of 9th Intern. Conf. in Automobile Dynamics and Strength
(MGTU "MAMI," Moscow, 2005),
pp. 19-25
[in Russian]. |
|
| Received |
15 December 2010 |
| Link to Fulltext |
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