MATLAB script and COMSOL models of the paper "Efficient wave analysis in multi-layered locally resonant metamaterials: A semi-analytical approach integrating dynamic homogenization"

The associated paper presents a semi-analytical framework that combines dynamic computational homogenization with an extended transfer matrix method (TMM) for efficient wave analysis in multi-layered locally resonant acoustic metamaterials (LRAMs). The approach allows modeling of complex multi-layered configurations involving arbitrary incidence angles and general microstructures, extending beyond the commonly adopted assumptions of symmetry and normal incidence.The proposed method first applies dynamic computational homogenization to derive the frequency-dependent homogenized enriched continuum of the LRAM, capturing inertial and mechanical effects through the dynamic impedance tensor. This enriched description is then incorporated into the extended TMM formulation to analyze wave transmission and reflection in layered setups with acoustic or elastic incoming media. The framework demonstrates excellent agreement with direct numerical simulations (DNS) in COMSOL, while providing significant computational efficiency.The MATLAB scripts include:Calculation of the frequency-dependent homogenized parameters of the LRAM unit cell.Evaluation of the effective impedance tensor describing the local resonance behaviour.Transmission and reflection analyses in multi-layered configurations with arbitrary incidence.The COMSOL models provide the DNS results used for validation and comparison.

相关论文提出了一套半解析框架，将动态计算均匀化（dynamic computational homogenization）与扩展传递矩阵法（extended transfer matrix method, TMM）相结合，用于高效分析多层局域共振声学超材料（multi-layered locally resonant acoustic metamaterials, LRAMs）中的波动问题。该方法可对包含任意入射角与通用微观结构的复杂多层构型进行建模，突破了现有研究普遍采用的对称性与正入射假设。
所提方法首先通过动态计算均匀化推导LRAMs的频域均匀化富集连续体模型，借助动态阻抗张量（dynamic impedance tensor）捕获惯性与力学效应。
随后将该富集描述纳入扩展TMM公式体系，以分析存在声学或弹性入射介质的层状结构中的波透射与反射行为。
该框架与COMSOL中的直接数值模拟（direct numerical simulations, DNS）结果吻合度极佳，同时具备显著的计算效率优势。
配套提供的MATLAB脚本可实现以下内容：LRAM胞元的频域均匀化参数计算、描述局域共振行为的有效阻抗张量求解，以及任意入射角下多层构型的透射与反射分析。
配套的COMSOL模型可生成用于验证与对比的直接数值模拟结果。