 | | 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: | | 13288 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8164
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| In English (Mech. Solids): | | 5124 |
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| I. G. Boruk, L. G. Lobas, and L. D. Patricio, "Equilibrium states of an inverted pendulum acted upon by a follower force on the elastically restrained upper end," Mech. Solids. 39 (5), 11-16 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
5 |
Pages |
11-16 |
| Title |
Equilibrium states of an inverted pendulum acted upon by a follower force on the elastically restrained upper end |
| Author(s) |
I. G. Boruk (Kiev, Covilia (Portugal))
L. G. Lobas (Kiev, Covilia (Portugal))
L. D. Patricio (Kiev, Covilia (Portugal)) |
| Abstract |
A model of an elastic beam subjected to a follower force represented by an inverted two-link pendulum with elastoviscous joints is studied. It is shown that a divergent bifurcation can occur at certain values of the magnitude of the follower force and stiffness of the elastic restraint. As a result of this bifurcation, the vertical equilibrium becomes unstable and two new non-vertical equilibrium states appear. This bifurcation is referred to as the fork bifurcation or triple equilibrium bifurcation. |
| References |
| 1. | H. Ziegler, "Die Srabilitäskriterien der Elastomechanik,"
Ing.-Arch, Bd. 20, H. 1, S. 49-56, 1952. |
| 2. | P. Hagedorn, "On the destabilizing effect of the nonlinear damping in non-conservative systems with follower forces,"
Int. J. Non-linear Mech., Vol. 5, No. 2, pp. 341-358, 1970. |
| 3. | Ya. G. Panovko and S. V. Sorokin, Quasi-stability of elastoviscous systems with follower forces,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 135-139, 1970. |
| 4. | H. Troger and A. Steindl,
Nonlinear Stability and Bifurcation Theory, Springer, Wien, New York, 1991. |
| 5. | S. A. Agafonov, "Stability and self-sustained vibrations of a double pendulum with elastic members under the action of a follower force,"
Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 185-190, 1992. |
| 6. | S. A. Agafonov, "Stabilization of the equilibrium of Ziegler's pendulum by means of parametric excitation,"
Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 36-40, 1997. |
| 7. | N. I. Zhinzher, "The influence of partial dissipation forces on the stability of elastic systems,"
Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 149-155, 1994. |
| 8. | A. P. Seiranyan, "Stabilization of non-conservative systems by dissipative forces and indeterminacy of the critical load,"
Doklady RAN, Vol. 348, No. 3, pp. 323-326, 1996. |
| 9. | N. N. Bautin, Behavior of Dynamical Systems Near Stability Region Boundaries [in Russian], Nauka, Moscow, 1984. |
| 10. | L. G. Lobas, "Nonlinear stability and fork-type bifurcations in dynamical systems with the simplest symmetry,"
PMM [Applied Mathematics and Mechanics], Vol. 60, No. 2, pp. 327-332, 1996. |
| 11. | A. M. Lyapunov, Collected Works. Volume 2 [in Russian], Izd-vo AN SSSR, Moscow, Leningrad, 1956. |
| 12. | V. G. Verbitskii and L. G. Lobas,
"Real bifurcations in two-link systems with rolling,"
PMM [Applied Mathematics and Mechanics], Vol. 60, No. 3, pp. 418-425, 1996. |
|
| Received |
21 January 2002 |
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