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

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.