Mechanics of metadamping in flexural dissipative metamaterials: Analysis and design in frequency and time domains
Mechanics of metadamping in flexural dissipative metamaterials: Analysis and design in frequency and time domains
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DOI：
10.1016/j.ijmecsci.2020.105459
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发表时间：
2020-05
影响因子：
7.3
通讯作者：
A. Aladwani;M. Nouh
中科院分区：
文献类型：
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作者：
A. Aladwani;M. Nouh
局部谐振超材料是具有有趣的声学缓解特性的工程结构，其源于入射弹性波和一组内部谐振之间的相互作用。通过阻尼增强，这些特性以独特且重要的方式变化，可以放大某些频率区域的波衰减能力，有时也可以减少它。文献中的耗散超材料的波色散力学通常是在波传播的背景下研究的，其中波数直接参与能带结构评估。在本文中，我们表明可以在结构振动的背景下进行此类研究，并演示给定有限周期结构的模态分析如何足以评估从代表性晶胞获得的预测的准确性。众所周知，自由波方法与复杂的频率解决方案相关，其中由于耗散而引起的衰减仅暂时发生，因此，可以构建频率和阻尼比带结构。在尝试建立无限和有限介质预测之间的直接相关性时，结果表明，给定晶胞的频率和阻尼比能带结构（即频率和阻尼比与波数关系）的组合会产生一种将阻尼比与波频率直接相关的新能带结构，该结构能够复制从相应有限结构中获得的发现。通过对具有阻尼宿主介质、阻尼谐振器及其组合的超材料梁进行一系列数值模拟，验证了在基本晶胞水平上遇到的不同现象。结果表明，与包括相同尺寸和形状的声子和均质结构的基线设计相比，整体阻尼水平以及阻尼源在决定局部谐振超材料中超阻尼的出现方面发挥着关键作用。最后，介绍了正负超阻尼的概念，并构建了相图，以指导和指导此类超材料在存在粘性和结构损失的情况下的设计。
Locally resonant metamaterials are engineered structures with intriguing acoustic mitigation properties which stem from an interplay between incident elastic waves and a set of internal resonances. Augmented with damping, such properties are shown to vary in unique and non-trivial ways which can amplify the wave attenuation capacity in certain frequency regions, as well as curtail it at times. Wave dispersion mechanics of dissipative metamaterials in literature are typically investigated in the context of wave propagation where the wavenumber is directly involved in band structure evaluations. In this paper, we show that it is possible to conduct such investigation in the context of structural vibrations and demonstrate how modal analysis of a given finite periodic structure is sufficient to assess the accuracy of the predictions obtained from a representative unit cell. The free wave approach is known to be associated with complex frequency solutions where attenuation due to dissipation takes place only temporally and as a consequence, frequency and damping ratio band structures can be constructed. In an attempt to establish direct correlations between infinite and finite medium predictions, it is shown that a combination of frequency and damping ratio band structures (i.e. frequency and damping ratio vs. wavenumber relations) for a given unit cell leads to a new band structure directly relating the damping ratio to wave frequency, which is capable of replicating the findings obtained from the corresponding finite structure. The different phenomena encountered at the fundamental unit cell level are validated via a series of numerical simulations of metamaterial beams with a damped host medium, damped resonators, as well as combinations thereof. The results reveal that the overall damping level as well as the damping source play key roles in dictating the metadamping emergence in locally resonant metamaterials as they compare to baseline designs including phononic and homogeneous structures of equal size and shape. Finally, the notion of positive and negative metadamping is introduced and phase diagrams are constructed to guide and inform the design of such metamaterials in the presence of viscous and structural losses.