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Nonlinear Waves in the Cosserat Continuum with Constrained Rotation

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Mechanics of Generalized Continua

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 7))

Abstract

The nonlinear viscoelastic micropolar medium with constrained rotation (the Cosserat pseudo-continuum) is considered. Using the method of bound normal waves, the original nonlinear system describing the dynamics of the medium is transferred to a system of evolutionary equations. It is shown that these evolutionary equations are four nonlinear partial differential equations two of which are the Burgers equations and the other two are the modified Korteweg-de Vries (mKdV) equations. The paper presents the results of the numerical study of nonlinear viscoelastic wave evolution.

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References

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Authors and Affiliations

  1. Nizhny Novgorod Branch of Blagonravov Mechanical Engineering Research Institute RAS, Belinskogo St. 85, 603024, Nizhny Novgorod, Russia

    Vladimir I. Erofeev & Sergey F. Sheshenin

  2. Saratov State Technical University, Politekhnicheskaja St. 77, 410054, Saratov, Russia

    Aleksandr I. Zemlyanukhin & Vladimir M. Catson

Authors
  1. Vladimir I. Erofeev
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  2. Aleksandr I. Zemlyanukhin
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  3. Vladimir M. Catson
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  4. Sergey F. Sheshenin
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Corresponding author

Correspondence to Vladimir I. Erofeev .

Editor information

Editors and Affiliations

  1. Halle-Wittenberg, Zentrum für Ingenieurwissenschaften, Martin-Luther-Universität, Kurt-Mothe-Str. 1, Halle (Saale), 06099, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. , Institut Jean Le Rond d’Alembert, UPMC (Paris), Tour 55, Place Jussieu 4, Paris Cedex 05, 75252, France

    Gérard A. Maugin

  3. IMASH RAN, Belinskogo str. 85, Nizhny Novgorod, 603024, Russian Federation

    Vladimir Erofeev

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Erofeev, V.I., Zemlyanukhin, A.I., Catson, V.M., Sheshenin, S.F. (2011). Nonlinear Waves in the Cosserat Continuum with Constrained Rotation. In: Altenbach, H., Maugin, G., Erofeev, V. (eds) Mechanics of Generalized Continua. Advanced Structured Materials, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19219-7_10

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