Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version)

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


 Web hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2013-2pp.151-158

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
In English (J. Appl. Math. Mech.): 799

<< Previous article | Volume 77, Issue 2 / 2013 | Next article >>
L.D. Akulenko and S.V. Nesterov, "Parametric oscillations and the stability of a mechanical system with considerable dissipation," J. Appl. Math. Mech. 77 (2), 151-158 (2013)
Year 2013 Volume 77 Issue 2 Pages 151-158
Title Parametric oscillations and the stability of a mechanical system with considerable dissipation
Author(s) L.D. Akulenko (Moscow, Russia, gavrikov@ipmnet.ru)
S.V. Nesterov (Moscow, Russia)
Abstract A detailed investigation is carried out into the problem of parametric oscillations when there is linear dissipation. Using constructive numerical-analytical methods, the boundaries of the domains of stability are constructed for a wide range of variation of the parameters, that is, the modulation factor and the friction coefficient. By solving non-self-adjoint eigenvalue and eigenfunction problems, the phase vectors of the three lower oscillation modes are determined and the principal features of the behaviour of the boundaries when the linear friction coefficient is varied are established. The eigenvalues and eigenfunctions of the adjoint boundary value problem are found. A complete biorthogonal system is constructed and its functional properties are determined. Modified expressions are obtained for scalar products and the squares of the norms of the characteristic phase vectors.
Received 28 November 2011
Link to Fulltext http://www.sciencedirect.com/science/article/pii/S0021892813000786
<< Previous article | Volume 77, Issue 2 / 2013 | 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 245, 119526 Moscow, Russia (+7 495) 434-2149 pmm@ipmnet.ru pmmedit@ipmnet.ru http://pmm.ipmnet.ru
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Journals on Mechanics Ltd.
© Journals on Mechanics Ltd.
Webmaster: Alexander Levitin
Rambler's Top100