 | | 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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| S. A. Agafonov and G. A. Shcheglov, "On the stabilization of a double pendulum acted upon by a follower force by means of parametric excitation," Mech. Solids. 38 (3), 27-35 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
3 |
Pages |
27-35 |
| Title |
On the stabilization of a double pendulum acted upon by a follower force by means of parametric excitation |
| Author(s) |
S. A. Agafonov (Moscow)
G. A. Shcheglov (Moscow) |
| Abstract |
For a double pendulum with linear viscoelastic joints
acted upon by a follower force,
it is shown that a parametric excitation applied to this system
can stabilize (under certain conditions) the unstable equilibrium
that appears in the system in the presence of small dissipation [1].
The application of two parametric excitations to this system leads
to a sharp increase in the number of possible parametric resonances,
in particular, to the appearance of parametric resonance
of multiplicity 2 [2].
In the present paper, two problems of stabilization of the equilibrium
of Ziegler's pendulum by means of two independent parametric excitations
are considered. In the first problem, the frequencies of the parametric
excitations are commensurable with the natural frequencies
of the pendulum. In the second problem, stabilization is implemented
by means of two high-frequency excitations. To solve this problem,
the results of [3] are utilized. It is shown that the region
of asymptotic stability can be increased either by one of the
two excitations or by two excitations acting simultaneously. |
| References |
| 1. | S. A. Agafonov, "Stabilization of the equilibrium
of Ziegler's pendulum by parametric excitation,"
Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 36-40, 1997. |
| 2. | S. V. Chelomei and G. A. Shcheglov, "On the dynamic stability
of a rectilinear pipe-line acted upon by a variable axial force due to the
flow of a pulsating fluid,"
Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 175-184, 1998. |
| 3. | S. A. Agafonov, "Stabilization of motion of non-conservative systems
by parametric excitation,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 199-202, 1998. |
| 4. | N. N. Bogolyubov and Yu. A. Mitropol'skii,
Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian],
Nauka, Moscow, 1974. |
|
| Received |
15 April 2002 |
| << Previous article | Volume 38, Issue 3 / 2003 | Next article >> |
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