Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2009-3pp.366-371

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 44, Issue 3 / 2009 | Next article >>
S. A. Agafonov, "On the stability of a circular system subjected to nonlinear dissipative forces," Mech. Solids. 44 (3), 366-371 (2009)
Year 2009 Volume 44 Number 3 Pages 366-371
DOI 10.3103/S0025654409030054
Title On the stability of a circular system subjected to nonlinear dissipative forces
Author(s) S. A. Agafonov (Bauman Moscow State Technical University, 2-ya Baumanskaya 5, Moscow, 105005 Russia)
Abstract A circular system is a mechanical system subjected to potential forces and positional nonconservative forces (circular forces). The latter linearly depend on the coordinates and are characterized by a skew-symmetric matrix. The influence of linear dissipative forces on the stability of a circular system is ambiguous: on the one hand, they can stabilize a stable circular system (making it asymptotically stable); on the other hand, they can destabilize it [1-4]. The action of linear dissipative forces on a circular system results in the so-called destabilization paradox: the stability threshold decreases by a finite value.

A detailed survey of this phenomenon can be found in [5]. The destabilization effect is also preserved under the action of nonlinear dissipative forces. The influence of these forces on the stability of the Ziegler pendulum with a tracking force was studied in [6]. It was shown that the critical value of the tracking force decreases by a finite value. A similar effect was discovered in the analysis of a continual system in [7].

In the present paper, we study how nonlinear dissipative forces affect the stability of the equilibrium of a circular mechanical system with two degrees of freedom. The stability problem is solved without any references to specific mechanical systems. The results are used to analyze the stability of a gimbal gyro with allowance for dry friction in the rotor bearings.
References
1.  S.A. Agafonov, "To the Stability of Nonconservative Systems," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 1, 47-51 (1986) [Mech. Solids (Engl. Transl.) 21 (1), 46-50 (1986)].
2.  D.R. Merkin, Introduction to Theory of Stability of Motion (Nauka, Moscow, 1971) [in Russian].
3.  O.N. Kirillov and A.P. Seyranian, "Stabilization and Destabilization of a Circulatory System by Small Velocity-Dependent Forces," J. Sound Vibr. 283 (3-5), 781-800 (2005).
4.  O.N. Kirillov, "A Theory of the Destabilization Paradox in Non-Conservative Systems," Acta Mech. 174 (3-4), 145-166 (2005).
5.  A.P. Seyranian, "Destabilization Paradox in Nonconservative Systems," Uspekhi Mekh. 13 (2), 89-124 (1990).
6.  P. Hagedorn, "On the Destabilizing Effect of Non-Linear Damping in Nonconservative Systems with Follower Forces," Int. J. Nonlin. Mech. 5 (2), 341-358 (1970).
7.  S.A. Agafonov and D.V. Georgievskii, "Dynamic Stability of a Beam That has Nonlinear Internal Viscosity and is Subjected to a Follower Force," Dokl. Ross. Akad. Nauk 396 (3), 339-342 (2004) [Dokl. Phys. (Engl. Transl.) 49 (5), 332-335 (2004)].
8.  G.V. Kamenkov, Selected Works, Vol. 1: \Motion Stability. Oscillations. Aerodynamics (Nauka, Moscow, 1971) [in Russian].
9.  L.G. Khazin and E.E. Shnol, Stability of Critical Equilibrium States (Center of Biological Studies, Pushchino, 1985) [in Russian].
10.  V.Ph. Zhuravlev, "Nutational Self-Oscillation of a Free Gyroscope," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 13-16 (1992) [Mech. Solids (Engl. Transl.) 27 (6), 11-14 (1992)].
Received 07 July 2005
Link to Fulltext
<< Previous article | Volume 44, Issue 3 / 2009 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100