Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2017, Volume 159, Book 4, Pages 429–443 (Mi uzku1418)  

This article is cited in 1 scientific paper (total in 1 paper)

Controlling the finite rotation of an elastic system from one state to another with vibration suppression at the final moment of operation

T. V. Grishaninaa, S. V. Russkikha, F. N. Shklyarchukb

a Moscow Aviation Institute (National Research University), Moscow, 125993 Russia
b Institute of Applied Mechanics, Russian Academy of Sciences, Moscow, 125040 Russia
References:
Abstract: The problem of passive control of an arbitrary elastic system that performs a finite rotation in the general case with acceleration or breaking about the unmovable axis and small nonstationary vibration under the impact of an arbitrarily distributed load proportional to some unknown finite function has been considered. The equations of motion of the system have been written in the normal coordinates which represent the eigenmodes of the free rotating system. In this case, the finite rotation of the system as an absolutely rigid body is represented by the zero mode. It is required that, at the end of the system rotation at the given angle and for the given time, elastic oscillations are eliminated for several lower eigenmodes. An unknown control function (control law) is sought for the considered time interval in the form of a series of sinuses (and also cosines) with unknown coefficients. On the basis of the exact solution of the equations in normal coordinates with initial and final conditions, the problem reduces to a system of linear algebraic equations for unknown coefficients. As an example, a roll rotation on a finite angle from one state of rest to another of spacecraft with two symmetrical multi-link solar panels has been considered. Calculations have been carried out for various numbers of eigenmodes to be eliminated with comparisons relative to the numerical solutions of the equations in generalized coordinates under the found control actions. It has been shown that in order to obtain a practically acceptable accuracy, it is sufficient to eliminate the vibrations of not more than two or three the lowest eigenmodes.
Keywords: vibration control, final turn of system, unsteady vibrations, suppression of elastic vibrations, solution in series, turn of a vehicle.
Funding agency Grant number
Russian Foundation for Basic Research 15-08-06259а
The work was supported in part by the Russian Foundation for Basic Research (project no. 15-08-06259a).
Received: 02.10.2017
Bibliographic databases:
Document Type: Article
UDC: 531.382
Language: Russian
Citation: T. V. Grishanina, S. V. Russkikh, F. N. Shklyarchuk, “Controlling the finite rotation of an elastic system from one state to another with vibration suppression at the final moment of operation”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 159, no. 4, Kazan University, Kazan, 2017, 429–443
Citation in format AMSBIB
\Bibitem{GriRusShk17}
\by T.~V.~Grishanina, S.~V.~Russkikh, F.~N.~Shklyarchuk
\paper Controlling the finite rotation of an elastic system from one state to another with vibration suppression at the final moment of operation
\serial Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
\yr 2017
\vol 159
\issue 4
\pages 429--443
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku1418}
\elib{https://elibrary.ru/item.asp?id=32819177}
Linking options:
  • https://www.mathnet.ru/eng/uzku1418
  • https://www.mathnet.ru/eng/uzku/v159/i4/p429
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
    Statistics & downloads:
    Abstract page:291
    Full-text PDF :136
    References:23
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024