International Applied Mechanics

, Volume 42, Issue 9, pp 997–1010

Similarities and differences between the Murnaghan and Signorini descriptions of the evolution of quadratically nonlinear hyperelastic plane waves

  • J. J. Rushchitsky
  • C. Cattani

DOI: 10.1007/s10778-006-0170-4

Cite this article as:
Rushchitsky, J.J. & Cattani, C. Int Appl Mech (2006) 42: 997. doi:10.1007/s10778-006-0170-4


An attempt is made to outline chronologically the five-stage development of the theory of nonlinear elastic waves. Next, attention is focused on the differences and similarities in the analytic description of polarized plane and cylindrical hyperelastic waves propagating in a nonlinear elastic material described by the Murnaghan model. Also, comparison is made of these waves when they propagate in materials described by the Murnaghan and Signorini potentials, which are rather different


nonlinear wave mechanics Murnaghan model Signorini model polarized elastic plane wave quadratically and cubically nonlinear wave equations similarities and differences of waves 

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • J. J. Rushchitsky
    • 1
  • C. Cattani
    • 1
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKiev

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