 | | 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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| V. I. Erofeev, V. V. Kazhaev, and N. P. Semerikova, "Torsional waves of finite amplitude in elastic rod," Mech. Solids. 42 (6), 974-979 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
6 |
Pages |
974-979 |
| Title |
Torsional waves of finite amplitude in elastic rod |
| Author(s) |
V. I. Erofeev (Nizhnii Novgorod Branch of Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Belinskogo 85, Nizhnii Novgorod, 603024, Russia, erf04@sinn.ru)
V. V. Kazhaev (Nizhnii Novgorod Branch of Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Belinskogo 85, Nizhnii Novgorod, 603024, Russia, wvs@dynamo.nnov.ru)
N. P. Semerikova (Nizhnii Novgorod Branch of Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Belinskogo 85, Nizhnii Novgorod, 603024, Russia) |
| Abstract |
We propose mathematical models generalizing the Coulomb and Vlasov equations of torsional vibrations of rods by taking the geometric nonlinearity into account. In the general case, the nonlinearity is taken into account both in the system of displacements (because the displacement vector in the case of rod torsion can be finite even for small strains) and in the relations between displacements and strains. We analyze nonlinear torsional stationary waves and find the effect of splitting of soliton-like unipolar waves in countercollisions. We also show that, in several cases, the existence of nonlinearities can also induce dispersion and that nonlinear stationary waves can also exist in the absence of dispersion in the linear medium. |
| References |
| 1. | A. I. Lurie,
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[in Russian]. |
| 2. | W. Nowacki,
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| 3. | I. I. Artobolevskii, Yu. I. Bobrovnitskii, and M. D. Genkin,
Introduction to Acoustic Dynamics of Mashinery
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| 4. | K. V. Frolov (Chairman of Editorial Board),
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V. V. Bolotin (Mashinostroenie, Moscow, 1999) [in Russian]. |
| 5. | V. I. Erofeev, V. V. Kazhaev, and N. P. Semerikova,
Waves in Rods. Dispersion. Dissipation. Nonlinearity
(Nauka, Fizmatlit, Moscow, 2002)
[in Russian]. |
| 6. | G. Whitham,
Linear and Nonlinear Waves
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| 7. | V. V. Kazhaev, A. I. Potapov, and N. P. Semerikova,
"Splitting up of Particle-Like Waves in Head-On Colisions,"
Izv. Vyssh. Uchebn. Zaved. Radiofiz.
38 (1-2), 100-105 (1995)
[Radiophysics and Quantum Electronics (Engl. Transl.)
38 (1-2), 67-70 (1995)]. |
| 8. | L. K. Zarembo and V. A. Krasil'nikov,
"Nonlinear Phenomena in the Propagation of Elastic Waves in Solids,"
Uspekhi Fiz. Nauk
102 (4), 549-586 (1970).
[Sov. Phys. Usp. (Engl. Transl.)
13 (6), 778-797 (1971)]. |
| 9. | D. R. Bland,
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(Mir, Moscow, 1972)
[in Russian]. |
| 10. | A. G. Kulikovskii and E. I. Sveshnikov,
Nonlinear Waves in Elastic Media
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[in Russian]. |
| 11. | R. Bullough and Ph. Caudry (Editors),
Solitons
(Springer, Heidelberg, 1980; Mir, Moscow, 1983). |
|
| Received |
20 January 2007 |
| Link to Fulltext |
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