MATLAB scripts of the paper "Efficient and accurate analysis of locally resonant acoustic metamaterial plates using computational homogenization"

The associated paper presents a 3D extension of the recently developed computational homogenization method for locally resonant acoustic metamaterial (LRAM) panels. The developed homogenization method provides a powerful computational tool for efficient and accurate analysis of LRAM panels of finite sizes and arbitrary shape under non-trivial excitations.<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 3D LRAM unit cell design. Finite element method is employed.2) Dispersion analysis of an infinite LRAM plate, using plane wave transformation.3) Frequency domain analysis of a finite LRAM plate, based on harmonic solution assumption. Isogeometric analysis is employed.4) Transient analysis of a finite LRAM plate. Isogeometric analysis is employed. Time integration is performed using Newmark method. 5) Application for the transient analysis of a large finite LRAM plate with a non-trivial non-harmonic excitation imposed. This analysis would be computationally prohibitive to perform by direct numerical simulation.Reference solutions for 2) by Bloch analysis in MATLAB and 3-4) by direct numerical simulations in COMSOL are given as well.

该相关论文提出了针对局域共振声学超材料（locally resonant acoustic metamaterial, LRAM）板的新近发展的计算均匀化方法的三维扩展版本。所开发的均匀化方法为非平凡激励下有限尺寸、任意形状的LRAM板的高效精准分析提供了强有力的计算工具。
上述方法已在MATLAB中实现，所提供的MATLAB脚本涵盖以下内容：
1. 针对给定三维LRAM胞元设计的与频率无关的动态有效材料特性计算，采用有限元法（finite element method）。
2. 无限LRAM板的色散分析，采用平面波变换法。
3. 基于谐波解假设的有限LRAM板的频域分析，采用等几何分析（isogeometric analysis）。
4. 有限LRAM板的瞬态分析，采用等几何分析，时间积分采用Newmark法（Newmark method）。
5. 施加非平凡非谐波激励的大型有限LRAM板的瞬态分析应用。此类分析若采用直接数值模拟，将面临极高的计算成本，几乎难以实现。
此外，本文还提供了通过MATLAB中布洛赫分析（Bloch analysis）得到的第2项任务的参考解，以及通过COMSOL中直接数值模拟得到的第3至4项任务的参考解。