 | | 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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| S. A. Agafonov and G. A. Shcheglov, "On the instability of a free elastic beam with non-linear internal viscosity under a follower force," Mech. Solids. 41 (2), 81-86 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
2 |
Pages |
81-86 |
| Title |
On the instability of a free elastic beam with non-linear internal viscosity under a follower force |
| Author(s) |
S. A. Agafonov
G. A. Shcheglov |
| Abstract |
Stability of elastic bodies and structural elements under
non-conservative loads is one of the subject areas in the mechanics
of deformable solids and stability theory which has been of
permanent interest through the entire past century [1-3].
In the literature on dynamic stability, a phenomenon called
"Ziegler's paradox" is well known. An infinitesimal viscosity in
linear non-conservative systems causes a decrease in the stability
boundary by a finite value. Similar phenomena are discussed in
detail, e.g., in the review [4]. In [5], the dynamic stability of a
beam with non-linear internal viscosity is studied. One end of the
beam is clamped, while the other end is subjected to a constant (in
magnitude) follower force. It is shown that the effect of decrease
in the stability boundary also takes place in the presence of
non-linear viscosity.
In the present paper, a free straight beam having non-linear
internal viscosity and loaded by a follower force at one end is
considered. It is shown that in this case the decrease in the
stability boundary takes place as well. |
| References |
| 1. | V. V. Bolotin, Non-conservative Problems of the Theory
of Elastic Stability [in Russian], Fizmatgiz, Moscow, 1961. |
| 2. | A. P. Filin, Applied Mechanics of Solids. Volume 3 [in Russian],
Nauka, Moscow, 1981. |
| 3. | N. Kh. Arutyunyan, A. D. Drozdov, and V. B. Kolmanovskii,
"Stability of viscoelastic bodies and structural members," in
Achievements in Science and Technology. Solid Mechanics [in Russian],
Vol. 19, pp. 3-77, VINITI, Moscow, 1987. |
| 4. | A. P. Seyranyan, "Destabilization paradox in the stability
problems for non-conservative systems," Uspekhi Mekhaniki [Advances
in Mechanics], Vol. 13, No. 2, pp. 89-124, 1990. |
| 5. | S. A. Agafonov and D. V. Georgievskii, "Dynamic stability
of a beam with non-linear internal
viscosity under a follower force," Doklady RAN, Vol. 396, No. 3,
pp. 339-342, 2004. |
| 6. | V. I. Feodos'ev, "On one stability problem," PMM [Applied Mathematics and Mechanics], Vol. 29,
No. 2, pp. 391-392, 1965. |
| 7. | L. G. Khazin and E. E. Shnol', Stability of Critical Equilibrium States [in Russian],
Center for Biological Studies of the USSR Academy of Sciences, Pushchino, 1985. |
|
| Received |
25 February 2005 |
| << Previous article | Volume 41, Issue 2 / 2006 | Next article >> |
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