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Archive of Applied Mechanics

, Volume 81, Issue 7, pp 925–942 | Cite as

Elements of study on dynamic materials

  • Martine RousseauEmail author
  • Gérard A. Maugin
  • Mihhail Berezovski
Original

Abstract

As a preliminary study to more complex situations of interest in small-scale technology, this paper envisages the elementary propagation properties of elastic waves in one-spatial dimension when some of the properties (mass density, elasticity) may vary suddenly in space or in time, the second case being of course more original. Combination of the two may be of even greater interest. Toward this goal, a critical examination of what happens to solutions at the crossing of pure space-like and time-like material discontinuities is given together with simple solutions for smooth transitions and numerical simulations in the discontinuous case. The effects on amplitude, speed of propagation, frequency changes and the appearance of a Doppler-like effect are demonstrated although the whole physical system remains linear.

Keywords

Dynamic materials Wave propagation Elasticity Inhomogeneity Interfaces Doppler effect 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Martine Rousseau
    • 1
    Email author
  • Gérard A. Maugin
    • 1
  • Mihhail Berezovski
    • 2
  1. 1.Université Pierre et Marie Curie, Institut Jean Le Rond d’Alembert, UMR CNRS 7190Paris Cedex 05France
  2. 2.Tallinn University of Technology, Center for Nonlinear ScienceTallinnEstonia

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