 | | 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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| A. V. Shatina, "Fast and slow dissipative evolution in mechanical systems containing viscoelastic elements," Mech. Solids. 39 (2), 10-17 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
2 |
Pages |
10-17 |
| Title |
Fast and slow dissipative evolution in mechanical systems containing viscoelastic elements |
| Author(s) |
A. V. Shatina (Moscow) |
| Abstract |
An asymptotic method is proposed for the analysis of the evolution of the
motion of mechanical systems containing viscoelastic elements. This method
combines the separation of motion for systems with infinite number of
degrees of freedom and the generalized Krylov-Bogolyubov method for
systems with fast and slow variables. The proposed method is a
development and generalization of the asymptotic method of [1]. It can be
applied to systems in which, apart from the perturbation due to the
elastic compliance and dissipation, there are small periodic perturbations
due to the external force field. As an example, the motion of a satellite
with flexible viscoelastic beams in a circular orbit is considered. |
| References |
| 1. | V. G. Vil'ke, "Separation of motions and averaging in the mechanics of
systems with infinite number of degrees of freedom," Vestnik MGU [Bulletin of
Moscow State University], Ser. 1. Matematika. Mekhanika, No. 5,
pp. 54-59, 1983. |
| 2. | V. G. Vil'ke, Analytical and Qualitative Methods in the Dynamics
of Systems with Infinite Number of Degrees of Freedom [in Russian],
Izd-vo MGU, Moscow, 1986. |
| 3. | F. L. Chernousko, "On the motion of a rigid body with elastic and
dissipative elements," PMM [Applied Mathematics and Mechanics], Vol. 42,
No. 1, pp. 34-42, 1978. |
| 4. | F. L. Chernousko, "On the motion of a viscoelastic solid about the
center of mass," Izv. AN SSSR. MTT [Mechanics of Solids], No. 1, pp. 22-26,
1980. |
| 5. | F. L. Chernousko and A. S. Shamaev, "Singular perturbation asymptotics
in dynamics of a rigid body with elastic and dissipative elements," Izv. AN
SSSR. MTT [Mechanics of Solids], No. 3, pp. 33-42, 1983. |
| 6. | E. V. Sinitsyn, "Singular perturbation
asymptotics in the study of the translational-rotational motion
of a viscoelastic body,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 1, pp. 104-110, 1991. |
| 7. | A. B. Vasil'eva and V. F. Butuzov, Asymptotic Expansions
of the Solutions of Singularly Perturbed Equations
[in Russian], Nauka, Moscow, 1973. |
| 8. | V. V. Sidorenko, "On the evolution of the motion of
a mechanical system with a linear damper having high rigidity,"
PMM [Applied Mathematics and Mechanics], Vol. 59, No. 4, pp. 562-568, 1995. |
| 9. | Yu. A. Mitropol'skii and O. B. Lykova, Integral Manifolds in Nonlinear
Mechanics [in Russian], Nauka, Moscow, 1973. |
| 10. | V. V. Strygin and V. A. Sobolev,
Separation of Motion by the Integral Manifold Method
[in Russian], Nauka, Moscow, 1988. |
| 11. | V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt, "Mathematical
aspects of the classical and celestial mechanics," in Modern Issues of
Mathematics. Fundamental Directions. Volume 3 [in Russian], VINITI, Moscow,
1985. |
|
| Received |
16 June 2001 |
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