多孔挠曲电型超材料板中的弯曲波分析

赵昊阳; 何状状; 张春利

doi:10.21656/1000-0887.450282

多孔挠曲电型超材料板中的弯曲波分析

doi: 10.21656/1000-0887.450282

赵昊阳^1,,
何状状^1,,
张春利^{1, 2, ,}

1.
浙江大学航空航天学院，杭州 310027
2.
浣江实验室，浙江诸暨 311816

(我刊青年编委张春利来稿)

基金项目:

国家重点研发计划 2020YFA0711701

详细信息

作者简介:
赵昊阳(2002—)，男，博士生(E-mail: 12424028@zju.edu.cn)

何状状(1996—)，男，博士生(E-mail: hezz@zju.edu.cn)

通讯作者:
张春利(1980—)，男，教授，博士，博士生导师(通讯作者. E-mail: zhangcl01@zju.edu.cn)

中图分类号: O343.5
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- 被引次数: 0
出版历程
- 收稿日期: 2024-10-21
- 修回日期: 2024-11-05
- 刊出日期: 2024-11-01

Bending Wave Analysis of Porous Flexoelectric Metamaterial Plates

1.
School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, P.R.China
2.
Huanjiang Laboratory, Zhuji, Zhejiang 311816, P.R.China

(Contributed by ZHANG Chunli, M.AMM Youth Editorial Board)

摘要

摘要: 多孔介电超材料由于内部孔洞导致应变的空间非均匀分布，特别是在孔洞边缘处应变梯度尤为显著，从而产生显著的挠曲电耦合效应. 因此，多孔介电超材料是一类具有挠曲电型力电耦合特性的智能超材料，有广阔的应用前景. 该文采用混合有限元法，研究了弯曲波在多孔挠曲电型超材料板中的传播特性，重点分析了孔径大小、孔的数量以及胞元内孔径梯度分布参数等因素对弹性波带隙结构的影响. 研究表明：由于挠曲电耦合效应使得整体结构的有效刚度增加，弯曲波带隙频率增高；随着孔径增大，弯曲波带隙频率降低，带隙宽度减小；随着孔洞数量增加，带隙频率逐渐降低，并出现带隙的“开-闭”现象；对于孔径呈梯度分布的多孔介电超材料板，梯度指数越大，弯曲波带隙的宽度越大.
- 挠曲电效应 /
- 弯曲波 /
- 带隙 /
- 多孔 /
- 超材料
Abstract: Porous dielectric metamaterials exhibit spatially non-uniform strain distribution due to internal pores with strain gradients particularly pronounced at the pore edges, leading to significant flexoelectric coupling effects. As a result, porous dielectric metamaterials represent a class of smart materials characterized by flexoelectric-type electromechanical coupling, showing great potential for various applications. A mixed finite element method (M-FEM) was employed to investigate the propagation characteristics of bending waves in porous flexoelectric metamaterial plates, aimed at the effects of pore sizes, pore numbers, and gradient distribution parameters of pore diameters within unit cells on the elastic wave bandgap structure. The results reveal that, the flexoelectric coupling effect enhances the effective stiffness of the structure, and thus increases the bending wave bandgap frequency; as the pore size increases, the bending wave bandgap frequency will decrease and the bandgap width will narrow; as the number of pores increases, the bandgap frequency will gradually decrease, and the bandgap will exhibit opening and closing phenomena; for porous dielectric metamaterial plates with gradient distributions of pore sizes, the larger the gradient index is, the wider the bending wave bandgap will be.
- flexoelectricity /
- flexural wave /
- band gap /
- porous /
- metamaterial
edited-by

edited-by
注释:

1) (我刊青年编委张春利来稿)

HTML全文

图 1 多孔超材料板示意图

Figure 1. The sketch of a porous metamaterial plate

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图 2 Q54单元示意图

Figure 2. The sketch of element Q54

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图 3 无限长PEEK板中的弯曲波带隙

Figure 3. The bandgap of flexural waves in an infinite PEEK plate

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图 4 弯曲波带隙结构

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 4. The bandgap structure of flexural waves

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图 5 孔径对弯曲波带隙位置的影响

Figure 5. Effects of the aperture diameter on the flexural wave bandgap position

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图 6 不同列数n下弯曲波第一、第二和第三带隙的上下边界频率体(R=15 nm)

Figure 6. The upper and lower edge frequencies of the 1st 3 flexural wave bandgaps for different n values (R=15 nm)

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图 7 不同梯度指数对弯曲波带隙的影响

Figure 7. Effects of different gradient indices on the bandgap of flexural waves

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表 1 PEEK材料的材料常数

Table 1. Material constants of PEEK

constant	value
tensile modulus E/GPa	3.6
Poisson’s ratio ν	0.38
flexoelectric coefficient f₁₁/(nC/m)	0.001 5
flexoelectric coefficient f₁₂/(nC/m)	17.61
flexoelectric coefficient f₄₄/(nC/m)	-0.019
density ρ/(kg/m³)	1 300
permittivity (ε₁₁=ε₃₃)/(nF/m)	3.079 5×10^-2

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