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Mathematical Problems in Engineering
Volume 2015, Article ID 475364, 12 pages
Research Article

Floquet-Bloch Theory and Its Application to the Dispersion Curves of Nonperiodic Layered Systems

1Hydrogeophysics and NDT Modelling Unit, University of Oviedo, C/Gonzalo Gutiérrez Quirós s/n, 33600 Mieres, Spain
2Dynamics Division, Applied Mechanics Department, Chalmers University of Technology, Hörsalsvägen 7, 41296 Gothenburg, Sweden

Received 20 October 2014; Revised 28 November 2014; Accepted 29 November 2014

Academic Editor: Xiao-Qiao He

Copyright © 2015 Pablo Gómez García and José-Paulino Fernández-Álvarez. 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.


Dispersion curves play a relevant role in nondestructive testing. They provide estimations of the elastic and geometrical parameters from experiments and offer a better perspective to explain the wave field behavior inside bodies. They are obtained by different methods. The Floquet-Bloch theory is presented as an alternative to them. The method is explained in an intuitive manner; it is compared to other frequently employed techniques, like searching root based algorithms or the multichannel analysis of surface waves methodology, and finally applied to fit the results of a real experiment. The Floquet-Bloch strategy computes the solution on a unit cell, whose influence is studied here. It is implemented in commercially finite element software and increasing the number of layers of the system does not bring additional numerical difficulties. The lateral unboundedness of the layers is implicitly taken care of, without having to resort to artificial extensions of the modelling domain designed to produce damping as happens with perfectly matched layers or absorbing regions. The study is performed for the single layer case and the results indicate that for unit cell aspect ratios under 0.2 accurate dispersion curves are obtained. The method is finally used to estimate the elastic parameters of a real steel slab.