基于材料选型的手性声学超材料带隙优化分析

陈炉云; 谢兴

doi:10.19693/j.issn.1673-3185.03078

基于材料选型的手性声学超材料带隙优化分析

doi: 10.19693/j.issn.1673-3185.03078

陈炉云^1, ,,
谢兴^2,

1.
上海交通大学海洋工程国家重点实验室，上海 200240
2.
武汉第二船舶设计研究所，湖北武汉 430205

基金项目: 高技术船舶科研计划资助项目(联装函[2016]548号)

详细信息

作者简介:
陈炉云，男，1975年生，博士，副研究员。研究方向：结构减振降噪新材料。E-mail：cluyun@sjtu.edu.cn

谢兴，男，1994年生，博士，工程师。研究方向：舰船结构设计与研究。E-mail：824506862@qq.com

通信作者:
陈炉云

中图分类号: U668.5；TB34
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出版历程
- 收稿日期: 2022-09-10
- 修回日期: 2022-12-31
- 网络出版日期: 2023-03-30
- 刊出日期: 2023-04-28

Bandgap optimization for chiral acoustic metamaterials based on material selection method

CHEN Luyun^{1
, ,},
XIE Xing^2
,

1.
State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
2.
Wuhan Second Ship Design and Research Institute, Wuhan 430205, China

基于材料选型的手性声学超材料带隙优化分析由陈炉云，等创作，采用知识共享署名4.0国际许可协议进行许可。

摘要

摘要: 目的旨在寻求扩大带隙频率范围，降低带隙起始频率的方法，分析并优化声学超材料的带隙。方法分析几何参数与材料参数对声学超材料带隙特性的影响，提出最大化带隙宽度方法。通过归一化带隙参数系数，将多目标优化问题转化为单目标优化问题。基于材料选型优化理论实现组分材料的转换，建立基于轻量化的手性声学超材料带隙参数优化方程。以六韧带手性声学超材料为例，定义散射体、韧带及包覆物等结构设计参数和材料参数为设计变量，开展声学超材料的结构参数−材料选型的综合优化。结果优化结果显示，带隙宽度增加了27.7%，下界频率减少了1048 Hz，初步达到了在声学超材料轻量化的基础上扩大带隙频率的目标；开展的有限长手性声学超材料结构的声传输分析验证了带隙优化方法的有效性。结论集成了结构参数−材料选型的综合优化可有效达到声学超材料轻量化的目标，研究成果可为新型声学超材料的设计提供技术参考。
- 声学超材料 /
- 材料选型 /
- 带隙优化 /
- 归一化 /
- 声传输
Abstract: Objectives This study seeks to expand the bandgap frequency band, reduce the bandgap starting frequency and analyze and optimize the bandgap parameters of acoustic metamaterials. Methods The influence of geometrical and material parameters on the bandgap properties of acoustic metamaterials is analyzed, and a method for maximizing the bandgap width is proposed. The multi-objective optimization problem is converted into a single objective optimization problem by normalizing the bandgap frequency coefficients. Structural material conversion is achieved via the material selection optimization method, and the optimization equations of bandgap parameters are established on the basis of weight-lightening. For chiral acoustic metamaterials, the material properties (density and wave velocity) and geometric parameters (scatterer diameter, ligament thickness and coating thickness) are defined as design variables, and the comprehensive optimization of structural parameters and material selection of acoustic metamaterials based on weight-lightening are implemented. Results The optimization results show that the bandgap width increases by 27.7% and the lower bound frequency decreases by 1048 Hz, thereby achieving the goal of expanding the bandgap width based on lightweight acoustic metamaterials. The acoustic transmission analysis of the finite chiral acoustic metamaterial structure is then carried out to verify the effectiveness of the proposed method. Conclusions The results show that the goal of lightweight acoustic metamaterials can be effectively achieved by integrating the comprehensive optimization of structural parameters and materials. As such, this study provides references for the design of new-type acoustic metamaterials.
- acoustic metamaterials /
- material selection /
- bandgaps optimization /
- normalizing /
- acoustic transmission

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图 1 六韧带手性声学超材料及布里渊区

Figure 1. Schematic diagram of hexachiral acoustic metamaterials and irreducible Brillouin area

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图 2 二维声学超材料有限元模型

Figure 2. Finite element model of two-dimensional hexachiral acoustic metamaterials

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图 3 六韧带声学超材料能带结构

Figure 3. Bandgap structure of hexachiral acoustic metamaterials

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图 4 声传输模型

Figure 4. Acoustic transmission model

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图 5 声传输损失系数

Figure 5. Acoustic transmission loss coefficients

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图 6 声压场对比

Figure 6. Comparison of the acoustic pressure distributions

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表 1 材料力学特性

Table 1. Mechanical properties of metamaterials

	选型材料名称	声速/(m·s⁻¹)	密度/(kg·m⁻²)	优化前材料	优化后材料
散射体	铅	2 160	11 600
	铜	4 726	8 960		铜
	钢	5 780	7 850	钢
	铝	5 095	2 730
韧带与包覆物	环氧树脂	2 680	1 180
	硬橡胶	2 300	1 200	环氧树脂
	软橡胶	300	1 300		软橡胶
	有机玻璃	1 180	2 680
基体	水	1 480	1 000	水	水

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表 2 优化结果对比

Table 2. Comparison of the optimization results

参数	初始设计	优化设计
带隙下界频率/Hz	49 362.5	48 314.2
带隙上界频率/Hz	62 277.1	64 815.4
带隙宽度/Hz	12 914.6	16 501.2
胞元质量/kg	0.008 8	0.006 9
归一化系数Ψ	1.000 00	1.149 73

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