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

Russian Academy of Sciences
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 Issues2011-1pp.49-55

Archive of Issues

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

<< Previous article | Volume 75, Issue 1 / 2011 | Next article >>
V.N. Paimushin and T.V. Polyakova, "The small free oscillations of a strip," J. Appl. Math. Mech. 75 (1), 49-55 (2011)
Year 2011 Volume 75 Issue 1 Pages 49-55
Title The small free oscillations of a strip
Author(s) V.N. Paimushin (Kazan, Russia,
T.V. Polyakova (Kazan, Russia)
Abstract The refined equations of the free oscillations of a rod-strip, constructed previously in a first approximation by reducing the two-dimensional equations to one-dimensional equations by using trigonometric basis functions and satisfying the static boundary conditions on the boundary surfaces are analysed. These equations, the solutions of which are obtained for the case of hinge-supported end sections of the rod, are split into two independent systems of equations. The first of these describe non-classical fixed longitudinal-transverse forms of free oscillations, which are accompanied by a distortion of the plane form of the cross section. It is shown that the oscillation frequencies corresponding to them depend considerably on Poisson's ratio and the modulus of elasticity in the transverse direction, while for a rod of average thickness for the same value of the frequency parameter (the tone) they may be considerably lower than the frequencies corresponding to the classical longitudinal forms of free oscillations, which are performed while preserving the plane form of the cross sections. The second system of equations describes transverse flexural-shear forms of free oscillations, whose frequencies decrease as the transverse shear modulus decreases. They are practically equivalent in quality and content to the similar equations of well-known versions of the refined theories, but, unlike them, when the number of the tone increases and the relative thickness parameter decreases they lead to the solutions of the classical theory of rods.
Received 5 February 2009
Link to Fulltext
<< Previous article | Volume 75, Issue 1 / 2011 | 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
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