Email this article Limited and Smooth Controls of Oscillations in Systems Given by Differential and Integro-Differential Equations
- Authors: Bobyleva T.N.1, Gusev I.M.2, Shamaev A.S.3
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Affiliations:
- Moscow State University of Civil Engineering
- Lomonosov Moscow State University
- Ishlinsky Institute for Problems in Mechanics RAS
- Issue: Vol 87, No 5 (2023)
- Pages: 820-828
- Section: Articles
- URL: https://journals.rcsi.science/0032-8235/article/view/232514
- DOI: https://doi.org/10.31857/S0032823523050053
- EDN: https://elibrary.ru/QHPNCH
- ID: 232514
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Abstract
The paper considers the problem of damping vibrations of a membrane and a plate with the help of forces distributed over their entire area. The proposed method allows us to consider restrictions not only on the absolute value of the control, but also on the absolute value of the derivatives of the functions that specify the control. Sufficient conditions are given for the initial conditions under which the problem of bringing the system to rest in a finite time is solvable, and the time of bringing to rest is estimated.
About the authors
T. N. Bobyleva
Moscow State University of Civil Engineering
Author for correspondence.
Email: tatyana2211@outlook.com
Russia, Moscow
I. M. Gusev
Lomonosov Moscow State University
Author for correspondence.
Email: gusevilya94@yandex.ru
Russia, Moscow
A. S. Shamaev
Ishlinsky Institute for Problems in Mechanics RAS
Author for correspondence.
Email: sham@rambler.ru
Russia, Moscow
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