 | | 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 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| Erofeev V.I. and Leontieva A.V., "Dispersion and Spatial Localization of Bending Waves Propagating in a Timoshenko Beam Laying on a Nonlinear Elastic Base," Mech. Solids. 56 (4), 443-454 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
4 |
Pages |
443-454 |
| DOI |
10.3103/S0025654421040051 |
| Title |
Dispersion and Spatial Localization of Bending Waves Propagating in a Timoshenko Beam Laying on a Nonlinear Elastic Base |
| Author(s) |
Erofeev V.I. (Mechanical Engineering Research Institute, Branch of Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences, Nizhniy Novgorod, 603024 Russia, erof.vi@yandex.ru)
Leontieva A.V. (Mechanical Engineering Research Institute, Branch of Federal Research Center Institute of Applied Physics of the Russian Academy of Sciences, Nizhniy Novgorod, 603024 Russia, aleonav@mail.ru) |
| Abstract |
In this article, we consider flexural (bending) waves propagating in a homogeneous beam fixed on a nonlinear elastic foundation. The dynamic behavior of the beam is determined by Timoshenko's theory. The system of equations describing the bending vibrations of the beam is reduced to a single nonlinear fourth-order equation for the transverse displacements of the beam median line particles. We state that if the beam stiffness is small compared to the linear stiffness of the foundation, the evolutionary equation is a modified Ostrovsky equation with an additional third-order nonlinear term. For the evolutionary equation, exact soliton solutions are found from the class of stationary waves in the form of a kink and an antikink. |
| Keywords |
flexural wave, Timoshenko beam, nonlinear elastic foundation, evolutionary equation, generalization of the modified Ostrovsky equation, nonlinear stationary wave, dispersion |
| Received |
25 May 2020 | Revised |
07 June 2020 | Accepted |
25 June 2020 |
| Link to Fulltext |
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