Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

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


IssuesArchive of Issues2001-5pp.25-30

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 36, Issue 5 / 2001 | Next article >>
A. G. Bagdoev and S. G. Saakyan, "Stability of nonlinear modulation waves in a magnetic field for the spatial and the averaged problems," Mech. Solids. 36 (5), 25-30 (2001)
Year 2001 Volume 36 Number 5 Pages 25-30
Title Stability of nonlinear modulation waves in a magnetic field for the spatial and the averaged problems
Author(s) A. G. Bagdoev (Erevan)
S. G. Saakyan (Erevan)
Abstract The linear problem of vibration of a magnetoelastic plate in a transverse magnetic field is considered in [1] in the framework of the Kirchhoff theory. A solution is obtained in the case of small electrical conductivity on the basis of the hypothesis of magnetoelasticity and without that hypothesis. In [2], this problem is solved under the assumption that the projection of the induced magnetic field onto the normal to the (nonperturbed) plate linearly depends on its normal component. By means of complicated calculations, a simple linear dispersion relation is obtained. In the case of small or large electrical conductivity, this relation transforms into known solutions. In [3], a linear solution is constructed for a plate of finite thickness. Nonlinear problems of stability of modulation waves in a longitudinal magnetic fields are solved in [4, 5]. The problems mentioned above have been studied on the basis of the classical theory of plates. In the present paper, two-dimensional modulation waves in a plate with finite conductivity in a magnetic field are studied by the method of simultaneously solving the equations of elasticity and those of magnetic induction. First, we consider the linear spatial problem of magnetoelasticity for a plate in a transverse magnetic field and obtain the corresponding dispersion relation. In the elastic case, this relation yields a known solution. In the case of small thickness and Alfven velocity, a simple dispersion relation is obtained. Next, we study the linear and nonlinear problems averaged over the thickness of the plate. The dispersion relation is also obtained for the spatial and the averaged problems for a plate in a longitudinal magnetic field. Conditions of stability of nonlinear waves are studied.
References
1.  S. A. Ambartsumyan, G. E. Bagdasaryan, and M. V. Belubekyan, Magnetoelasticity of Thin Shells and Plates [in Russian], Nauka, Moscow, 1977.
2.  S. A. Ambartsumyan and G. E. Bagdasaryan, Electroconductive Plates and Shells in a Magnetic Field [in Russian], Nauka, Moscow, 1996.
3.  S. A. Ambartsumyan and M. V. Belubekyan, Vibrations and Stability of Current-carrying Elastic Plates [in Russian], National Academy of Sciences of Armenia, Erevan, 1992.
4.  A. G. Bagdoev and L. A. Movsesyan, "Nonlinear vibrations of plates in a longitudinal magnetic field," Izv. AN ArmSSR, Mekhanika, Vol. 35, No. 1, pp. 16-22, 1982.
5.  A. G. Bagdoev and L. A. Movsesyan, "Modulations of thermal magnetoelastic waves in nonlinear plates," Izv. AN ArmSSR, Mekhanika, Vol. 52, No. 1, pp. 25-30, 1999.
6.  W. Nowacki, Theory of Elasticity [Russian translation], Mir, Moscow, 1975.
7.  H. Kauderer, Nonlinear Mechanics [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1961.
8.  R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morries, Solitons and Nonlinear Wave Equations [Russian translation], Mir, Moscow, 1988.
9.  V. I. Karpman, Nonlinear Waves in Dispersive Media [in Russian], Nauka, Moscow, 1973.
Received 20 January 2000
<< Previous article | Volume 36, Issue 5 / 2001 | 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 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100