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arXiv 1701.02431physics.class-phcond-mat.othermath.OC
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有限长声学超材料中局域共振带隙的形成:一个封闭形式的传递函数模型

Formation of Local Resonance Band Gaps in Finite Acoustic Metamaterials: A Closed-form Transfer Function Model

H. Al Ba'ba'a, M. Nouh, T. Singh

摘要:

本文的目的是利用传递函数来理解局部共振声学超材料中带隙的形成。确定了一个递归的方法,为任何数量的串联布置的局部谐振质量的质量单元,推导出一个封闭的形式的传递函数的表达式。端到端传递函数的分析有助于确定有限超材料中带隙形成的基本机制。该机制包括(a)位于各个局部谐振器的固有频率处的重复复共轭零点,(b)位于带隙侧面的两个极点的存在,以及(c)带隙中极点的不存在。的有限单元动力学分析相比,无限长的超材料的布洛赫波分析,以确认的理论极限的带隙估计的传递函数建模。该分析还解释了带隙如何随着超材料链中单元数量的增加而演变,并强调了响应如何根据沿超材料长度选择的传感位置而变化。建议的传递函数方法来计算和评估带隙的局部谐振结构提供了一个框架,利用控制技术来修改和调整带隙的有限的超材料实现。

英文摘要:

The objective of this paper is to use transfer functions to comprehend the formation of band gaps in locally resonant acoustic metamaterials. Identifying a recursive approach for any number of serially arranged locally resonant mass in mass cells, a closed form expression for the transfer function is derived. Analysis of the end-to-end transfer function helps identify the fundamental mechanism for the band gap formation in a finite metamaterial. This mechanism includes (a) repeated complex conjugate zeros located at the natural frequency of the individual local resonators, (b) the presence of two poles which flank the band gap, and (c) the absence of poles in the band-gap. Analysis of the finite cell dynamics are compared to the Bloch-wave analysis of infinitely long metamaterials to confirm the theoretical limits of the band gap estimated by the transfer function modeling. The analysis also explains how the band gap evolves as the number of cells in the metamaterial chain increases and highlights how the response varies depending on the chosen sensing location along the length of the metamaterial. The proposed transfer function approach to compute and evaluate band gaps in locally resonant structures provides a framework for the exploitation of control techniques to modify and tune band gaps in finite metamaterial realizations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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