MATLAB scripts of the paper "Homogenized enriched continuum analysis of acoustic metamaterials with negative stiffness and double negative effects"

The associated paper demonstrates, for the first time, the application of a recently developed computational homogenization method towards dynamic analyses of locally resonant acoustic metamaterials (LRAM) exhibiting double negative effects, i.e. simultaneously negative mass and negative stiffness effects within a certain frequency regime. The present method provides an efficient tool for analyses of double negative metamaterials involving non-trivial loading and complex unit cell design.<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) Calculation of the dispersion spectra of an infinite LRAM medium, using plane wave transformation. Reference solution by Bloch analysis is given as well.3) Frequency domain analysis of a LRAM prism embedded in a conventional material domain, based on harmonic solution assumption. Individual compressive and shear wave fields are determined as well, using Helmholtz decomposition. Finite element method is employed.

本关联论文首次将新近提出的计算均匀化方法应用于具有双负效应的局域共振声学超材料（locally resonant acoustic metamaterials, LRAM）的动力学分析，这类超材料在特定频域范围内可同时呈现负质量与负刚度效应。本方法为涉及非平凡载荷与复杂胞元设计的双负超材料分析提供了高效工具。
上述方法基于MATLAB实现，配套提供的MATLAB脚本包含以下内容：1) 针对给定LRAM胞元设计，计算其与频率无关的动态有效材料属性，计算过程采用有限元法（Finite Element Method）。2) 采用平面波变换，计算无限大LRAM介质的色散谱，同时给出基于布洛赫分析（Bloch analysis）的参考解。3) 基于简谐解假设，对嵌入常规材料域中的LRAM棱柱体开展频域分析；同时采用亥姆霍兹分解（Helmholtz decomposition）求解各自的压缩波与剪切波场，计算过程同样采用有限元法。