 | | 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. I. Munitsyn, "Nonlinear vibrations of a thread with a strainer," Mech. Solids. 36 (2), 20-25 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
2 |
Pages |
20-25 |
| Title |
Nonlinear vibrations of a thread with a strainer |
| Author(s) |
A. I. Munitsyn (Ivanovo) |
| Abstract |
3D nonlinear vibrations of a thread are investigated
in the case where the thread passes through a strainer
providing a preselected tension force. The thread is assumed to be
inextensible, the nonlinearity of the system is due to the variation of
the length of the thread involved in the motion.
Two solutions of the natural vibration mode problem have been
found near the first natural frequency. One of these solutions corresponds
to a planar motion of the thread, whereas the second solution represents the
circular motion of the thread points. We study forced vibrations of
the thread under a kinematic excitation in one plane, as well as in
two mutually perpendicular planes. The dissipation is taken into account
in accordance with the external friction model. The stability of the
solutions obtained is investigated. The results of the numerical simulation,
obtained with the first three terms of the expansion of the solution in
terms of the coordinates being taken into account, are presented by the
amplitude-frequency characteristics. |
| References |
| 1. | L. D. Akulenko and S. V. Nesterov, "Nonlinear vibrations of a
string," Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 87-92, 1993. |
| 2. | L. D. Akulenko and S. V. Nesterov, "Forced nonlinear
vibrations of a string," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 17-24,
1996. |
| 3. | L. D. Akulenko, G. V. Kostin, and S. V. Nesterov, "The influence of
dissipation on nonlinear 3D vibrations of a string," Izv. AN. MTT [Mechanics of Solids], No. 1,
pp. 19-28, 1997. |
| 4. | G. V. Anand, "Stability of nonlinear vibration of stretched
strings," J. Acoust. Soc. America, Vol. 46, No. 3, pp. 667-677, 1969. |
| 5. | D. R. Merkin, Introduction to the Mechanics of a Flexible
Thread [in Russian], Nauka, Moscow, 1960. |
| 6. | V. A. Svetlitskii, Mechanics of Flexible Strings and Threads
[in Russian], Mashinostroenie, Moscow, 1978. |
| 7. | V. I. Gulyaev, V. A. Bazhenov, and S. L. Popov, "Applied
Problems of the Theory of Nonlinear Vibrations of Mechanical Systems
[in Russian], Vysshaya Shkola, Moscow, 1989. |
|
| Received |
14 October 1998 |
| << Previous article | Volume 36, Issue 2 / 2001 | Next article >> |
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