[论文解读] Low-frequency wide band-gap elastic/acoustic meta-materials using the K-damping concept

Ioannis Antoniadis, Eleni Chatzi+4 more|arXiv (Cornell University)|Apr 29, 2017

Acoustic Wave Phenomena Research参考文献 28被引用 3

一句话总结

本文提出了一种低频弹性/声学超材料中的新型K-阻尼概念，用负刚度元件替代了内部沉重的质量块，实现了宽禁带和增强的阻尼效果，且无需增加大量附加质量。该方法利用局域共振与负刚度，实现显著的振动与波抑制，通过一维质量-质量晶格中的布洛赫理论和模态分析得到验证。

ABSTRACT

The terms "acoustic/elastic meta-materials" describe a class of periodic structures with unit cells exhibiting local resonance. This localized resonant structure has been shown to result in negative effective stiffness and/or mass at frequency ranges close to these local resonances. As a result, these structures present unusual wave propagation properties at wavelengths well below the regime corresponding to band-gap generation based on spatial periodicity, (i.e. "Bragg scattering"). Therefore, acoustic/elastic meta-materials can lead to applications, especially suitable in the low-frequency range. However, low frequency range applications of such meta-materials require very heavy internal moving masses, as well as additional constraints at the amplitudes of the internally oscillating locally resonating structures, which may prohibit their practical implementation. In order to resolve this disadvantage, the K-Damping concept will be analyzed. According to this concept, the acoustic/elastic meta-materials are designed to include negative stiffness elements instead or in addition to the internally resonating added masses. This concept removes the need for the heavy locally added heavy masses, while it simultaneously exploits the negative stiffness damping phenomenon. Application of both Bloch's theory and the classical modal analysis at the one-dimensional mass-in-mass lattice is analyzed and corresponding dispersion relations are derived. The results indicate significant advantages over the conventional mass-in-a mass lattice, such as broader band-gaps and increased damping ratio and reveal significant potential in the proposed solution. Preliminary feasibility analysis for seismic meta-structures and low frequency acoustic isolation-damping confirm the strong potential and applicability of this concept.

研究动机与目标

• 克服传统质量-质量超材料在低频振动吸收中需依赖沉重内部质量块的局限性。
• 解决局部共振结构中因高质心和大振幅约束带来的实际实施挑战。
• 提出一种利用负刚度元件（K-阻尼）的设计策略，实现宽禁带和高阻尼比，且无需增加质量。
• 通过一维晶格中色散关系和模态行为的理论分析，验证K-阻尼概念。
• 展示其在地震超结构和声学隔离等低频应用中的可行性。

提出的方法

• K-阻尼概念将负刚度元件引入周期性弹性/声学超材料的元胞中，替代或补充传统的附加质量块。
• 应用布洛赫理论分析波传播并推导含负刚度的一维质量-质量晶格的色散关系。
• 采用经典模态分析评估系统的动态行为与阻尼特性。
• 通过理论模型对比K-阻尼结构与传统质量-质量系统的性能，评估禁带宽度与阻尼比。
• 利用局域共振增强负刚度，实现有效负刚度与等效质量特性。
• 结合数值与解析推导，验证宽禁带的出现及阻尼性能的提升。

实验结果

研究问题

• RQ1 负刚度元件能否有效替代低频弹性/声学超材料中的沉重内部质量块？
• RQ2 在含负刚度的一维质量-质量晶格中，负刚度的引入如何影响禁带宽度？
• RQ3 与传统质量-质量超材料相比，K-阻尼概念在多大程度上提升了阻尼比？
• RQ4 负刚度对周期性超材料中波传播与局域化有何影响？
• RQ5 K-阻尼概念能否实现低频振动与声学隔离的实际应用？

主要发现

• K-阻尼概念可在不依赖沉重内部质量块的前提下，实现低频弹性/声学超材料中的宽禁带。
• 与传统质量-质量配置相比，该系统表现出显著提高的阻尼比。
• 通过布洛赫理论推导的色散关系证实，由于局域共振与负刚度的共同作用，出现了宽广的禁带。
• 理论分析表明，负刚度增强了波的衰减与局域化，从而提升了隔振性能。
• 初步可行性研究证实，该概念在地震超结构与低频声学隔离中具有强大应用潜力。