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Shock and Vibration
Volume 2, Issue 2, Pages 173-190
http://dx.doi.org/10.3233/SAV-1995-2208
Review

Waves, Solids, and Nonlinearities

Jüri Engelbrecht

Institute of Cybernetics, Estonian Academy of Sciences, EE0026 Tallinn, Estonia

Received 8 July 1994; Accepted 14 September 1994

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this article nonlinearity is taken as a basic property of continua or any other wave-bearing system. The analysis includes the conventional wave propagation problems and also the wave phenomena that are not described by traditional hyperbolic mathematical models. The basic concepts of continuum mechanics and the possible sources of nonlinearities are briefly discussed. It is shown that the technique of evolution equations leads to physically well-explained results provided the basic models are hyperbolic. Complicated constitutive behavior and complicated geometry lead to mathematical models of different character and, as shown by numerous examples, other methods are then used for the analysis. It is also shown that propagating instabilities possess wave properties and in this case the modeling of energy redistribution has a great importance. Finally, some new directions in the theory and applications are indicated.