 | | 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.A. Gavrikov and G.V. Kostin, "Bending Vibrations of an Elastic Rod Controlled by Piezoelectric Forces," Mech. Solids. 58 (8), 2803-2817 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
8 |
Pages |
2803-2817 |
| DOI |
10.3103/S0025654423080204 |
| Title |
Bending Vibrations of an Elastic Rod Controlled by Piezoelectric Forces |
| Author(s) |
A.A. Gavrikov (Ishlinsky Institute of Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia, stepan_vasenin@mail.ru)
G.V. Kostin (Ishlinsky Institute of Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia, reshmin@ipmnet.ru) |
| Abstract |
In this paper, we study a two-mass controlled mechanical system consisting of a supporting
disk rotating around its axis fixed in space and a carried ring attached to the disk using weightless elastic elements. There are no dampers in the system. Suppression of radial vibrations is considered from
the perspective of optimal control theory. On sufficiently large time intervals, Newton’s numerical
method is used to solve the boundary value problem of Pontryagin’s maximum principle. The properties of the phase trajectories of the system are studied depending on the initial states of the disk and
ring and the number of springs in a complex model of elastic interaction. Under certain initial conditions and parameters of the system, the trajectory of the center of mass of the ring is shown to tend to
a circle due to the radiality of the elastic force and the conservation law of kinetic momentum. The
indicated tendency to reach the circular motion mode is not uniform and depends on the number of
springs. It is demonstrated that, at a small number of elastic elements, the trajectory of the ring does
not take the form of a circle, while almost complete damping of radial vibrations occurs. For the system parameters considered during the numerical experiment, the control is established to be relay with
a sufficiently large number of switchings. In this case, the entire system is simultaneously spinning-up. |
| Keywords |
relay control, maximum principle, controlled rotation, boundary value problem, Newton’s method, vibration damping |
| Received |
01 September 2023 | Revised |
01 October 2023 | Accepted |
10 October 2023 |
| Link to Fulltext |
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