 | | 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. Vlakhova and I. V. Novozhilov, "Separation of motions in a mechanical system with different frequencies that does not contain small or large parameters in an explicit form," Mech. Solids. 38 (1), 33-40 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
1 |
Pages |
33-40 |
| Title |
Separation of motions in a mechanical system with different frequencies that does not contain small or large parameters in an explicit form |
| Author(s) |
A. V. Vlakhova (Moscow)
I. V. Novozhilov (Moscow) |
| Abstract |
We consider a linear system close to a conservative system
with eigenfrequencies strongly different in absolute values.
Unlike [1, 2], the original equations of motion do not
contain small parameters or large stiffness coefficients in
an explicit form. We construct two versions of an approximate
mathematical model governing the motion with respect to
the low-frequency components under the action of slow disturbances.
To reduce the problem to the Tikhonov singularly perturbed form
we previously pass to the normal coordinates for the conservative
part of the system. |
| References |
| 1. | F. L. Chernousko, "Dynamics of systems with
elastic members of high stiffness,"
Izv. AN SSSR. MTT [Mechanics of Solids],
No. 4, pp. 101-113, 1983. |
| 2. | I. V. Novozhilov, "A limiting model for a system
with elastic members of high stiffness,"
Izv. AN SSSR. MTT [Mechanics of Solids],
No. 4, pp. 24-27, 1988. |
| 3. | B. V. Bulgakov, Vibrations [in Russian],
Gostekhizdat, Moscow, 1954. |
| 4. | I. V. Novozhilov, Fractional Analysis [in Russian],
Izd-vo MGU, Moscow, 1995. |
| 5. | A. N. Tikhonov, "Systems of differential equations with
small parameters at the derivatives,"
Matem. Sbornik, Vol. 31(73), No. 3, pp. 575-586, 1952. |
| 6. | A. B. Vasil'eva and V. F. Butuzov,
Asymptotic Expansions of Solutions of Singularly Perturbed
Equations [in Russian],
Nauka, Moscow, 1973. |
| 7. | A. I. Klimushev and N. N. Krasovskii,
"Uniform asymptotic stability of systems of differential equations
with a small parameter at higher-order derivatives,"
PMM [Applied Mathematics and Mechanics], Vol. 25, No. 4, pp. 680-690, 1961. |
| 8. | N. N. Bukhgol'ts, Fundamental Course in Theoretical Mechanics.
Part 2 [in Russian], Nauka, Moscow, 1972. |
|
| Received |
08 November 2000 |
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