附着式局域共振声子晶体薄板的带隙解析解

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摘要声子晶体作为一种具有超材料特性的复合减振材料，其带隙范围的计算一直是研究的重点，目前主要的计算方法都是数值方法，得到的带隙范围依赖于系统参数的选取，而带隙的设计只能采取参数试凑或优化的方法。针对以上问题，根据局域共振型声子晶体薄板的动力学方程，得到系统振动位移的解析解。在此基础上，得到了阻抗表达式，并根据阻抗的概念阐述了带隙的形成机理，讨论了系统阻尼对带隙的影响，得到了无阻尼条件下带隙的解析解，所得结果与有限元及平面波展开法的计算结果一致。利用带隙解析解，可以非常方便地设计局域共振声子晶体薄板的带隙，为声子晶体的研究和应用提供了全新的方法。

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	杨文
	陈凯伦
	郭旭
	陈泽宇
	刘长利

关键词 ：声子晶体薄板, 局域共振, 带隙解析解

Abstract：Phononic crystal is a kind of composite vibration-reduction material with metamaterial characteristics, and its band gap calculation has always been a hot research topic. At present, the main calculation methods are numerical methods. The band gap range depends on system parameters selection. Band gap design can only adopt parameter trial and error or optimization methods. For the above problems, the analytical solution of system vibration displacement was obtained according to the dynamic equation of locally resonance phononic crystal(LR PC) thin plate. On this basis, according to impedance concept, band gap formation mechanism was explained, system damping influence on the band gap was discussed, and band gap analytical solution under undamped conditions was obtained, which were consistent with finite element method and plane wave expansion method. Using this band gap analytical solution, designing band gap of LR PC thin plate can be convenient, which provides a new method for phononic crystal research and application.

Key words： phononic crystal thin plate locally resonant band gap analytical solution

收稿日期: 2020-12-29 出版日期: 2022-04-28

引用本文:

杨文，陈凯伦，郭旭，陈泽宇，刘长利. 附着式局域共振声子晶体薄板的带隙解析解[J]. 振动与冲击, 2022, 41(8): 238-243.
YANG Wen, CHEN Kailun, GUO Xu, CHEN Zeyu, LIU Changli. Analytical solution of band gap in an attached locally resonant phononic crystal thin plate. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(8): 238-243.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I8/238

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