MATLAB scripts of the paper "Computational homogenization of locally resonant acoustic metamaterial panels towards enriched continuum beam/shell structures"

The associated paper presents a novel computational homogenization method enabling efficient and accurate modelling of wave propagation phenomena in locally resonant acoustic metamaterial (LRAM) panels, which was not possible for direct numerical simulations as well as available homogenization methods. The proposed method provides a considerable advantage for fast analyses and design of metamaterial panels.<br>The method above is implemented in MATLAB and the provided MATLAB scripts include:1) Calculation of the frequency-independent dynamic effective material properties for a given LRAM unit cell design. Finite element method is employed.2) Dispersion analysis of an infinite LRAM beam, using plane wave transformation.3) Frequency domain analysis of a finite LRAM beam, based on harmonic solution assumption. Isogeometric analysis is employed.4) Transient analysis of a finite LRAM beam. Isogeometric analysis is employed. Time integration is performed using Newmark method. Reference solutions by direct numerical simulations using COMSOL are given as well.

本关联论文提出了一种新颖的计算均匀化方法，可实现局域共振声学超材料（locally resonant acoustic metamaterial, LRAM）板中波传播现象的高效精准建模，而直接数值模拟与现有均匀化方法均无法完成此类建模。所提方法为超材料板的快速分析与设计带来了显著优势。
上述方法已基于MATLAB实现，所提供的MATLAB脚本包含以下内容：
1）针对给定LRAM胞元设计，计算与频率无关的动态有效材料属性，该计算采用有限元法（finite element method）；
2）采用平面波变换，对无限长LRAM梁开展色散分析；
3）基于谐波解假设，对有限长LRAM梁进行频域分析，该分析采用等几何分析（isogeometric analysis）；
4）对有限长LRAM梁进行瞬态分析，同样采用等几何分析，时间积分过程通过Newmark法完成。
此外还提供了使用COMSOL进行直接数值模拟得到的参考解。