局域共振声学超材料对弹性波宽频带隙形成与调控机制研究

The lattice constant of locally resonance-bansed acoustic metamaterials (or called locally resonant phononic crystal) can be 1-2 orders of magnitude lower than wavelength in its spectral gaps which induced by Bragg scattering phononic crystal. This characteristic can be used to modulation long classical elastic wave by composite material of small dimensions. Though the theoretical calculation has indicated that band gap can be broadened by close-packed structure,the present studies mostly aimed at resonant scattering unit, while there were very few systemic studies on the influence of structural factor. This results in producing band gap just at certain narrow frequency in locally resonance-based acoustic metamaterials. With the further development of locally resonance-based acoustic metamaterials, narrow band gap cannot satisfy modulated elastic wave requirements in wide frequency anymore. To solve this conflict, influence of structural factor need to be studied. Wide-band gaps of locally resonance-based acoustic metamaterials are suitably studied by woodpile structure due to large parameter tuning range and complex preparation. Moreover, introduced grade, which can achieve new degrees of freedom in the construction of woodpile structure, may further broaden band gap. Therefore, the formation and modulation of wide-band gap in locally resonance-based acoustic metamaterials will be investigated deeply by the grade woodpile structure that evaluate the influence of structural factor. The research results will be meaningful in both modulating wide-band gaps of acoustic metamaterials and control elastic wave in its engineering application.

局域共振声学超材料（或称局域共振声子晶体）的晶格尺寸可以比布拉格散射声子晶体产生的禁带波长小1-2个数量级，具有利用小尺寸控制大波长的能力，可广泛应用于新型声波波导，滤波器以及声开关等器件的设计与制造。虽然密排结构可以拓宽局域共振声学超材料的带隙频率，但是现有研究多针对共振散射单元，缺乏对结构的系统研究，这导致它只能产生窄频带隙。随着局域共振声学超材料的发展，较窄的带隙范围已不能满足弹性波宽频调控日益增长的需求。为了解决这一问题，需要在研究中考虑结构因素的影响。木堆结构参数调节范围宽，制备方法简单，是研究局域共振声学超材料宽频带隙形成与调控机制的理想结构。此外，梯度化还可以引入新的色散调节自由度，能进一步扩大带隙调控范围。因此，本项目利用可以评估结构因素影响的梯度木堆结构，深入研究局域共振声学超材料宽频带隙形成与调控机制，将对超材料宽频带隙的调节和工程应用中弹性波的调控提供重要的参考价值。

局域共振声学超材料（或称局域共振声子晶体）的晶格尺寸可以比布拉格散射声子晶体产生的禁带波长小1-2个数量级，具有利用小尺寸控制大波长的能力，可广泛应用于新型声波波导，滤波器以及声开关等器件的设计与制造。现有研究多针对共振散射单元，缺乏对结构的系统研究，这导致它只能产生窄频带隙。为了解决这一问题，本项目利用木堆结构等多振子耦合系统深入研究了局域共振声学超材料宽频带隙形成与调控机制。首先在一维质量弹簧模型中，引入附加振子构成多振子耦合系统，由于振子之间的耦合作用，不仅使一维质量弹簧系统的带隙分化成两个，且上截止频率向高频移动，使原有带隙得到有效拓宽，并增加了带隙的调控因素。将振子耦合系统拓展至三维局域共振木堆结构，计算结果证实由于正交共振子（剪切共振子与压缩共振子）之间的耦合作用，并将带隙拓宽了128Hz。进一步的研究表明，带隙宽度与振子间耦合作用强度有关，可以利用杆宽度、梯度等参数对带隙结构进行调节。在此基础上，本课题还构建了基于同心圆环结构的二维单振子、双振子及三振子声学超材料系统。研究发现随着振子数量的增加，偶极子振动方式增多，在更多的频率范围内呈现负的等效质量密度，使带隙数目增多。但由于振子间耦合强度偏弱，带隙并没有得到有效拓宽，与其相比木堆结构在拓宽局域共振结构带隙具有明显优势。当考虑材料粘弹性时，利用木堆结构宽频特性，制备了一种宽频水下吸声材料。数值计算与实验结果表明局域共振声子木堆能够在宽频范围内获得优异的低频吸声性能。木堆结构为解决局域共振型水下吸声材料的减重设计提供了新思路。本课题提出的局域共振木堆结构可以在宽频范围内对声波产生带隙或强吸收效应，为局域共振声学超材料的带隙工程研究及新型水下吸声材料的设计提供了新的思路。