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IssuesArchive of Issues2003-5pp.122-126

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V. I. Erofeev and N. V. Klyueva, "Propagation of Nonlinear Torsional Waves in a Beam Made of a Different-Modulus Material," Mech. Solids. 38 (5), 122-126 (2003)
Year 2003 Volume 38 Number 5 Pages 122-126
Title Propagation of Nonlinear Torsional Waves in a Beam Made of a Different-Modulus Material
Author(s) V. I. Erofeev (Nizhni Novgorod)
N. V. Klyueva (Nizhni Novgorod)
Abstract The influence of different-modulus property of a material on the propagation of torsional waves in a beam is studied, with warping being taken into account. In contrast to common structural elastic materials exhibiting weak nonlinearity in the working stress range, different-modulus materials demonstrate strong nonlinearity even for relatively small strains. These materials are interesting in connection with the investigation of nonlinear waves in elastic media, in particular, of such curious wave objects as solitons. It seems that actual observation of solitons is only possible in strongly nonlinear media.

The different-modulus property leads to quadratic nonlinearity of torsional waves. For nonlinear steady-state strain waves (periodic ones and solitons) we obtain relations between the basic parameters of such waves (amplitude, wave-length, wave propagation speed, and the coefficient of nonlinear distortion of the wave shape). It is shown that together with the classical behavior of solitons, with a wave of a larger amplitude having smaller width and propagating with a higher speed, anomalous behavior of solitons can be observed.
References
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2.  R. M. Jones and D. A. Nelson, "A comparison of theory with experiment for material models for nonlinear deformation of graphite," Raketn. Tekhn. i Kosmonavt., Vol. 14, No. 10, pp. 101-113, 1976.
3.  V. A. Lyakhovskii and V. P. Myasnikov, Different-modulus phenomenon, anisotropy, and reflecting boundaries," Izv. AN SSSR. Fizika Zemli, No. 11, pp. 69-73, 1986.
4.  E. V. Lomakin and Yu. N. Rabotnov, "Elasticity relations for isotropic different-modulus bodies," Izv. AN SSSR. MTT [Mechanics of Solids], No. 6, pp. 29-34, 1978.
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7.  V. A. Lyakhovskii and V. P. Myasnikov, "On the behavior of an elastic medium with micro-defects," Izv. AN SSSR. Fizika Zemli, No. 10, pp. 71-75, 1984.
8.  V. A. Gasilov, M. V. Golovin, V. P. Myasnikov, and A. Kh. Pergament, "Analysis of the stress-strain state of rock on the basis of the different-modulus model of continuum," Matem. Modelirov., Vol. 11, No. 1, pp. 39-44, 1999.
9.  V. P. Myasnikov and A. I. Oleinikov, "Basic general relations of a model of an isotropic elastic different-strength medium," Doklady AN, Vol. 322, No. 1, pp. 57-60, 1992.
10.  V. A. Gasilov, M. V. Golovin, V. P. Myasnikov, and A. Kh. Pergament, "The different-modulus model of continuum as applied to the behavior of rocks under high stresses," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 86-92, 2000.
11.  E. V. Lomakin and M. P. Kazantsev, "Specific features of torsion of beams made of materials whose properties depend on the structure of the stress state," Vestnik MGU [Bulletin of Moscow State University], Ser. 1. Mat., Mekh, No. 2, pp. 56-61, 1995.
12.  E. V. Lomakin, "Torsion of beams made of materials with elastic properties depending on the structure of the stress state," Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 30-38, 2002.
13.  V. I. Erofeev, N. V. Klyueva, S. A. Monichev, and N. P. Semerikova, "Effect of different-modulus property of the material and warping on torsional wave propagation in a beam," in Testing Materials and Structures. Collection of articles [in Russian], pp. 117-136, Intelservis, NF IMASh RAN, Nizhni Novgorod, 2000.
14.  V. I. Erofeev and S. A. Monichev, "Longitudinal and torsional vibrations of beams made of different-modulus materials," Problemy Mashinostr. i Nadezhn., No. 1, pp. 3-7, 1999.
15.  V. I. Erofeev, V. V. Kazhaev, N. P. Semerikova, Waves in Beams: Dispersion, Dissipation, and Nonlinearity [in Russian], Fizmatlit, Moscow, 2002.
Received 24 April 2001
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