Dispersion diagrams play a crucial role in examining, analyzing and designing wave propagation in periodic structures. Despite their ubiquity and current research interest, introductory papers and reference scripting tailored to novel researchers in the field are lacking. This paper aims to address this gap, by presenting a comprehensive educational resource for researchers starting in the field of periodic structures and more specifically on the study of dispersion relations captured by dispersion surfaces or curves in dispersion diagrams. The objective is twofold. A first objective is to give a detailed explanation of dispersion diagrams, with graphical illustrations. Secondly, a documented code is provided to compute dispersion curves of 3D structures with 2D periodicity using the so-called inverse approach. These dispersion curves are obtained with numerical simulations using the finite element method. The code is written for elastic wave propagation and orthogonal periodicity directions, but can be extended to other types of linear wave propagation, non-orthogonal periodicity directions or 1D and 3D periodicity. The aim of this code is to serve as a starting point for novice researchers in the field, to facilitate their understanding of different aspects of dispersion diagrams and serve as a stepping stone in their future research.

中文翻译：

---

数值色散曲线计算指南：解释、解释和基本 Matlab 代码

色散图在检查、分析和设计周期性结构中的波传播方面发挥着至关重要的作用。尽管它们无处不在并且当前的研究兴趣很大，但针对该领域的新研究人员量身定制的介绍性论文和参考脚本却很缺乏。本文旨在弥补这一差距，为周期结构领域的研究人员提供全面的教育资源，更具体地说，研究由色散面或色散图中的曲线捕获的色散关系。目标是双重的。第一个目标是通过图示对色散图进行详细解释。其次，提供了记录的代码，用于使用所谓的逆方法计算具有 2D 周期性的 3D 结构的色散曲线。这些色散曲线是使用有限元方法通过数值模拟获得的。该代码是针对弹性波传播和正交周期性方向编写的，但可以扩展到其他类型的线性波传播、非正交周期性方向或 1D 和 3D 周期性。该代码的目的是作为该领域的新手研究人员的起点，促进他们对色散图不同方面的理解，并作为他们未来研究的垫脚石。