Dynamic Properties of Essentially Nonlinear Generalized Continua

  • Alexey V. Porubov
  • Eron L. Aero
  • B. R. Andrievsky
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)


Essentially nonlinear proper structural model for continua with internal structure is analyzed using the localized strain wave solutions of the governing equations for macro- and micro-strains. The intervals of the velocity are found when either compression or tensile localized strain waves exist. It is obtained that simultaneous existence of compression and tensile macro-strain waves is impossible in contrast to the micro-strains responsible for the lattice defects. Also, it is shown that similar profiles of the macro-strain solitary waves may be accompanied by distinct profiles of the micro-strain waves. Generation of the bell-shaped defects in the lattice is studied numerically that allows us to describe structural deviations caused by the dynamical loading due to the localized macro-strain wave propagation.


Solitary Wave Localize Wave Exact Travel Wave Solution Neighboring Peak Tensile Wave 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Alexey V. Porubov
    • 1
  • Eron L. Aero
    • 1
  • B. R. Andrievsky
    • 1
  1. 1.Institute of Problems in Mechanical EngineeringSt. PetersburgRussia

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