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


IssuesArchive of Issues2008-6pp.715-723

Archive of Issues

Total articles in the database: 10482
In Russian (ÏÌÌ): 9683
In English (J. Appl. Math. Mech.): 799

<< Previous article | Volume 72, Issue 6 / 2008 | Next article >>
A.G. Kulikovskii and Ye.I. Sveshnikova, "A model for describing near-resonance oscillations in an elastic layer," J. Appl. Math. Mech. 72 (6), 715-723 (2008)
Year 2008 Volume 72 Issue 6 Pages 715-723
Title A model for describing near-resonance oscillations in an elastic layer
Author(s) A.G. Kulikovskii (Moscow, Russia, kulik@mi.ras.ru)
Ye.I. Sveshnikova (Moscow, Russia, sveshn@mech.mat.msu.su)
Abstract One-dimensional transverse oscillations in a layer of a non-linear elastic medium are considered, when one of the boundaries is subjected to external actions, causing periodic changes in both tangential components of the velocity. In a mode close to resonance, the non-linear properties of the medium may lead to a slow change in the form of the oscillations as the number of the reflections from the layer boundaries increases. Differential equations describing this process were previously derived. The equations obtained are hyperbolic and the change in the solution may both keep the functions continuous and lead to the formation of jumps. In this paper a model of the evolution of the wave patterns is constructed as integral equations having the form of conservation laws, which determine the change in the functions describing the oscillations of the layer as “slow” time increases. The system of hyperbolic differential equations previously obtained follows from these conservation laws for continuous motions, in which one of the variables is slow time, for which one period of the actual time serves as an infinitesimal quantity, while the second variable is the real time. For the discontinuous solutions of the same integral equations, conditions on the discontinuity are obtained. An analogy is established between the solutions of the equations obtained and non-linear waves propagating in an unbounded uniform elastic medium with a certain chosen elastic potential. This analogy enable discontinuities which may be physically realised to be distinguished. The problem of steady oscillations of an elastic layer is discussed.
Received 08 April 2008
Link to Fulltext
<< Previous article | Volume 72, Issue 6 / 2008 | 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 https://pmm.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Journal of Applied Mathematics and Mechanics
webmaster
Rambler's Top100