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首页> 外文期刊>Mathematical Problems in Engineering >Floquet-Bloch Theory and Its Application to the Dispersion Curves of Nonperiodic Layered Systems
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Floquet-Bloch Theory and Its Application to the Dispersion Curves of Nonperiodic Layered Systems

机译：Floquet-Bloch理论及其在非周期性分层系统色散曲线中的应用

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摘要

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.
机译：色散曲线在无损检测中起着重要的作用。它们提供了实验中的弹性和几何参数的估计值，并为解释体内波场行为提供了更好的视角。它们是通过不同的方法获得的。提出了Floquet-Bloch理论来替代它们。该方法以直观的方式进行解释；它将其与其他常用技术（例如基于搜索根的算法或表面波的多通道分析方法）进行比较，并最终应用于拟合真实实验的结果。 Floquet-Bloch策略在单位单元上计算解决方案，此处将研究其影响。它是在商业有限元软件中实现的，增加系统的层数不会带来额外的数值困难。隐含地处理了层的横向无边界，而不必求助于建模域的人工扩展，该建模域设计为产生与完全匹配的层或吸收区域相同的阻尼。该研究是针对单层情况进行的，结果表明，在0.2色散曲线下，晶胞的纵横比得到了精确的值。最后，该方法用于估计真实钢坯的弹性参数。

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