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Philosophical Magazine Volume 85, 2005 - Issue 33-35: Recent Advances in Theoretical Mechanics. Guest Editors: Dimitris Lagoudas, Paul Steinmann and Esteban Busso
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Original Articles

Waves in microstructured materials and dispersion

J. Engelbrecht Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn Technical University, Tallinn, EstoniaCorrespondence[email protected]
,
A. Berezovski Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn Technical University, Tallinn, Estonia
,
F. Pastrone Department of Mathematics, University of Turin, Turin, Italy
&
M. Braun Chair of Mechanics, University Duisburg-Essen, Duisburg, Germany
Pages 4127-4141 | Received 20 Apr 2004, Accepted 22 Nov 2004, Published online: 21 Feb 2007
 
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Abstract

The dispersive effects due to the presence of microstructure in solids are studied. The basic mathematical model is derived following Mindlin's theory. In the one-dimensional case the governing equations of a linear system are presented. An approximation using the slaving principle indicates a hierarchy of waves. The corresponding dispersion relations are compared with each other. The choice between the models can be made on the basis of physical effects described by dispersion relations.

Acknowledgements

Support from the Estonian Science Foundation, MIUR COFIN 2002 and the ESF NATEMIS Programme is gratefully acknowledged. One of the authors (J.E.) would like to thank the A. v. Humboldt Foundation for support in 2003.

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