The so-called Locally Resonant Acoustic Metamaterials (LRAM) are considered for the design of specifically engineered devices capable of stopping waves from propagating in certain frequency regions (bandgaps), this making them applicable for acoustic insulation purposes. This fact has inspired the design of a new kind of lightweight acoustic insulation panels with the ability to attenuate noise sources in the low frequency range (below 5000 Hz) without requiring thick pieces of very dense materials. A design procedure based on different computational mechanics tools, namely, (1) a multiscale homogenization framework, (2) model order reduction strategies and (3) topological optimization procedures, is proposed. It aims at attenuating sound waves through the panel for a target set of resonance frequencies as well as maximizing the associated bandgaps. The resulting design's performance is later studied by introducing viscoelastic properties in the coating phase, in order to both analyse their effects on the overall design and account for more realistic behaviour. The study displays the emerging field of Computational Material Design (CMD) as a computational mechanics area with enormous potential for the design of metamaterial-based industrial acoustic parts.

中文翻译：

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局部共振声学超材料的计算设计

所谓的局部共振声学超材料 (LRAM) 被考虑用于设计能够阻止波在某些频率区域（带隙）中传播的专门工程设备，这使得它们适用于隔音目的。这一事实启发了一种新型轻质隔音板的设计，该板能够衰减低频范围（低于 5000 Hz）的噪声源，而无需使用非常致密的厚片材料。提出了一种基于不同计算力学工具的设计程序，即（1）多尺度均匀化框架，（2）模型降阶策略和（3）拓扑优化程序。它旨在通过面板衰减一组目标共振频率的声波，并最大化相关的带隙。随后通过在涂层阶段引入粘弹性特性来研究最终设计的性能，以便分析它们对整体设计的影响并考虑更现实的行为。该研究将计算材料设计 (CMD) 的新兴领域展示为一个计算力学领域，对于基于超材料的工业声学部件的设计具有巨大潜力。