 | | 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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| A. P. Ivanov and V. I. Pereverzev, "Analysis of a two-mass vibroimpact system with an elastic bond," Mech. Solids. 36 (4), 32-39 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
4 |
Pages |
32-39 |
| Title |
Analysis of a two-mass vibroimpact system with an elastic bond |
| Author(s) |
A. P. Ivanov (Moscow)
V. I. Pereverzev (Moscow) |
| Abstract |
We consider a collinear system that consists of two particles
moving between two walls. One of the particles is attached to
one of the walls by means of a spring, while the other moves freely,
colliding with the other wall and the first particle.
From the physics point of view, this system
can serve as a model of the interaction of an ideal gas with
the walls of the vessel, with the molecular structure of the walls
and their motion being taken into account. From the mathematics point
of view, this system generalizes Ulam's problem
of the acceleration of cosmic rays [1] and is a modification of
"Andreev's hammer" in which one spring is replaced by a rigid
limiter.
We construct simple periodic motions of the system for the case
of fixed walls, investigate their stability and discuss bifurcations.
A qualitative analysis of the system dynamics is carried out for the case
where the ratio of the masses of the particles is small. The evolution
of the system with slowly moving walls is discussed. |
| References |
| 1. | A. J. Lichtenberg and M. A. Lieberman, Regular
and Stochastic Motion [Russian translation], Mir, Moscow, 1984. |
| 2. | A. E. Kobrinskii and A. A. Kobrinskii, Two-dimensional
Vibroimpact Systems [in Russian], Nauka, Moscow, 1981. |
| 3. | A. P. Ivanov, Dynamics of Systems with Mechanical Impacts
[in Russian], Mezhdunarodnaya Programma Obrazovaniya, Moscow, 1997. |
| 4. | J. Guckenheimer and Ph. Holmes, Nonlinear Oscillations,
Dynamical Systems, and Bifurcations of Vector Fields,
Springer, New York, 1993. |
| 5. | P. Appel, Theoretical Mechanics [Russian translation],
Vol. 2, Fizmatgiz, Moscow, 1960. |
| 6. | A. P. Ivanov and A. P. Markeev, "On the dynamics of systems
with unilateral constraints," PMM [Applied Mathematics and Mechanics],
Vol. 48, No. 4, pp. 632-636, 1984. |
| 7. | V. Ph. Zhuravlev, "Equations of motion for mechanical systems
with ideal unilateral constraints,"
PMM [Applied Mathematics and Mechanics], Vol. 42, No. 5, pp. 781-788, 1978. |
| 8. | E. T. Whittaker, Analytical Dynamics [Russian translation],
Gostekhizdat, Moscow, Leningrad, 1937. |
| 9. | A. P. Markeev, Theoretical Mechanics [in Russian],
Nauka, Moscow, 1990. |
| 10. | A. P. Markeev, Libration Points in Celestial Mechanics
and Space Flight Dynamics [in Russian],
Nauka, Moscow, 1978. |
| 11. | V. I. Arnold, Mathematical Methods of Classical Mechanics
[in Russian], Nauka, Moscow, 1979. |
| 12. | V. I. Arnold, V. V. Kozlov, and A. I. Neishtadt,
"Mathematical aspects of classical and celestial mechanics,"
in Achievements in Science and Technology. Modern Problems of Mathematics.
Fundamental Directions. Volume 3 [in Russian], VINITI, Moscow, 1985. |
|
| Received |
25 May 1999 |
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