 | | 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: | | 11262 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3251 |
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| << Previous article | Volume 55, Issue 8 / 2020 | Next article >> |
| Erofeev V.I. and Leonteva A.V., "Anharmonic Waves in a Mindlin–Herrmann Rod Immersed in a Nonlinearly Elastic Medium," Mech. Solids. 55 (8), 1284-1297 (2020) |
| Year |
2020 |
Volume |
55 |
Number |
8 |
Pages |
1284-1297 |
| DOI |
10.3103/S0025654420080087 |
| Title |
Anharmonic Waves in a Mindlin–Herrmann Rod Immersed in a Nonlinearly Elastic Medium |
| Author(s) |
Erofeev V.I. (Mechanical Engineering Research Institute, Russian Academy of Sciences, Nizhny Novgorod, 603000 Russia, erof.vi@yandex.ru)
Leonteva A.V. (Mechanical Engineering Research Institute, Russian Academy of Sciences, Nizhny Novgorod, 603000 Russia, aleonav@mail.ru) |
| Abstract |
Propagation of longitudinal waves in a Mindlin–Herrmann rod immersed in a nonlinearly
elastic medium is studied. Various options of the stiffness ratio of the rod and external medium in
which the rod is placed are considered and three limiting cases are obtained. It is shown that, if the
stiffness of the external medium significantly exceeds the rod stiffness, then the evolutionary equation
becomes the Ostrovsky equation that is well-known in the nonlinear dynamics. The equation has no
exact solutions, but allows a qualitative study when the senior derivative is equal to zero. In this case,
the solution in the form of a nonlinear periodic stationary wave is found and analyzed. If the stiffness
of external medium is significantly lower than the rod stiffness, then the evolutionary equation is the
equation different from the Ostrovsky equation in the nonlinear part. In this case, it is demonstrated
soliton propagation of a classical profile in the rod is possible. It is pointed out that, when the stiffnesses of external medium and rod are of the same order of magnitude, the nonlinear stationary waves
cannot be generated. |
| Keywords |
longitudinal wave, Mindlin–Herrmann model, nonlinearly elastic medium, Ostrovsky evolutionary equation, periodic wave, soliton |
| Received |
06 August 2019 | Revised |
27 April 2020 | Accepted |
06 May 2020 |
| Link to Fulltext |
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