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IssuesArchive of Issues2007-6pp.974-979

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Total articles in the database: 9179
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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, Nonlinear Theory of Elasticity (Nauka, Moscow, 1980) [in Russian].
2.  W. Nowacki, Theory of Elasticity (PWN, Warsaw, 1970; Mir, Moscow, 1975).
3.  I. I. Artobolevskii, Yu. I. Bobrovnitskii, and M. D. Genkin, Introduction to Acoustic Dynamics of Mashinery (Nauka, Moscow, 1979) [in Russian].
4.  K. V. Frolov (Chairman of Editorial Board), Vibrations in Technology. Reference Book in 6 Volumes, Vol. 1: Vibrations of Linear Systems, 2nd ed., Ed. by 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 (Wiley, New York, 1974; Mir, Moscow, 1977).
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, Nonlinear Dynamical Elasticity (Mir, Moscow, 1972) [in Russian].
10.  A. G. Kulikovskii and E. I. Sveshnikov, Nonlinear Waves in Elastic Media (Moskov. Litsei, Moscow, 1998) [in Russian].
11.  R. Bullough and Ph. Caudry (Editors), Solitons (Springer, Heidelberg, 1980; Mir, Moscow, 1983).
Received 20 January 2007
Link to Fulltext http://www.springerlink.com/content/9t748j7313h0550u
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