挠曲电声子晶体梁的波动特性分析

杨莎莎; 孔燚帆; 沈承

doi:10.21656/1000-0887.460003

挠曲电声子晶体梁的波动特性分析

doi: 10.21656/1000-0887.460003

杨莎莎^{1, 2,},
孔燚帆^{2, 3},
沈承^{2, 3, ,}

1.
南京工业职业技术大学机械工程学院，南京 210023
2.
南京航空航天大学航空航天结构力学及控制全国重点实验室，南京 210016
3.
南京航空航天大学多功能轻量化材料与结构工信部重点实验室，南京 210016

基金项目:

国家自然科学基金 12202183

国家自然科学基金 12472089

国家重点研发计划 2023YFB4604800

详细信息

作者简介:
杨莎莎(1986—)，女，校聘副教授，博士(E-mail: 2016100849@niit.edu.cn)

通讯作者:
沈承(1986—)，男，副教授，博士，硕士生导师(通讯作者. E-mail: cshen@nuaa.edu.cn)

中图分类号: O32
计量
- 文章访问数: 28
- HTML全文浏览量: 2
- PDF下载量: 7
- 被引次数: 0
出版历程
- 收稿日期: 2025-01-07
- 修回日期: 2025-02-15
- 刊出日期: 2025-08-01

Analysis of Wave Propagation Properties of Flexoelectric Phononic Crystal Beams

YANG Shasha^{1, 2
,},
KONG Yifan^{2, 3},
SHEN Cheng^{2, 3
, ,}

1.
School of Mechanical Engineering, Nanjing University of Industry Technology, Nanjing 210023, P.R.China
2.
State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China
3.
MIIT Key Laboratory of Multifunctional Lightweight Materials and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China

摘要

摘要: 当结构尺度减小到微纳米尺寸时，一种新型的力电耦合效应(即挠曲电效应)愈发重要. 建立了在微尺寸下考虑挠曲电效应的声子晶体梁模型，研究了结构的色散曲线以及振动响应. 首先基于挠曲电效应的纳米电介质理论，从电学Gibbs自由能密度出发，得到了挠曲电材料的本构方程. 并基于Bernoulli-Euler梁的理论假设和变分原理推导出考虑挠曲电效应、微惯性效应以及动挠曲电效应的梁的振动控制方程. 通过传递矩阵法计算考虑了挠曲电效应的声子晶体梁的能带结构，以及有限长悬臂梁的固有频率. 研究了挠曲电效应以及结构参数对固有频率和带隙的影响规律. 结果表明，挠曲电效应显著提高了固有频率，可通过改变结构参数来获得更宽带隙. 仿真结果与理论结果吻合较好，验证了理论方法的有效性. 该文工作可为今后考虑挠曲电效应的微纳米声子晶体梁的设计提供理论指导.
- 挠曲电效应 /
- 声子晶体梁 /
- 色散曲线 /
- 固有频率 /
- 传递矩阵
Abstract: When the structural scale is reduced to the micro and nano sizes, a new type of electromechanical coupling effect (i.e. the flexoelectric effect) becomes increasingly important. A phononic crystal beam model with the flexoelectric effect in micro scale was established. The dispersion curves and vibration responses of the structure were studied. Based on the nanodielectric theory under flexoelectric effects, the constitutive equation for flexoelectric materials was derived from the electrical Gibbs free energy density. Based on the theoretical hypothesis of the Bernoulli-Euler beam and the variational principle, the governing vibration equation for the beam under flexoelectric effects, micro-inertial effects and dynamic flexoelectric effects, was derived. The energy band structure of a phonon crystal beam under flexoelectric effects and the natural frequencies of a finite length cantilever beam were calculated with the transfer matrix method. The flexoelectric effects and the influences of structural parameters on natural frequencies and band gaps were studied. The results show that, the flexoelectric effect significantly increases the natural frequency, and the wider band gap can be obtained by the change of the structural parameters. The simulation results are in good agreement with the theoretical ones, which proves the validity of the theoretical method. The work provides a theoretical guidance for the future design of micro and nano phonon crystal beams under the flexoelectric effects.
- flexoelectric effect /
- phononic crystal beam /
- dispersion curve /
- natural frequency /
- transfer matrix
other
(Recommended by LIU Shaobao, M.AMM Editorial Board)
注释:

1) (我刊编委刘少宝推荐)

HTML全文

图 1 挠曲电声子晶体梁示意图

Figure 1. Schematic of the flexoelectric phononic crystal beam

下载: 全尺寸图片幻灯片

图 2 材料A和B的横截面尺寸

Figure 2. Cross sections of materials A and B

下载: 全尺寸图片幻灯片

图 3 考虑各种微观效应的声子晶体梁色散曲线

Figure 3. Dispersion curves of phononic crystal beams under various microscopic effects

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图 4 第一带隙频率随单胞长度变化曲线

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. Variations of the 1st gap frequencies with cell lengths

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图 5 单胞数以及厚度比对梁固有频率的影响曲线

Figure 5. Influence curves of cell numbers and thickness ratios on natural frequencies of the beam

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图 6 挠曲电效应与厚度比对声子晶体梁固有频率的影响

Figure 6. Influences of the flexoelectric effect and thickness ratio on natural frequencies of the phonon crystal beam

下载: 全尺寸图片幻灯片

图 7 单胞数以及长度比对梁固有频率的影响曲线

Figure 7. Influence curves of cell numbers and length ratios on natural frequencies of the beam

下载: 全尺寸图片幻灯片

图 8 挠曲电效应与长度比对声子晶体梁固有频率的影响

Figure 8. Influences of the flexoelectric effect and the length ratio on natural frequencies of the phonon crystal beam

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图 9 第一禁带带宽变化曲线

Figure 9. Variation curves of the 1st bandgap bandwidth

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图 10 第一禁带中心频率变化曲线

Figure 10. Variation curves of center frequency of the 1st bandgap

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图 11 COMSOL有限元仿真与理论计算结果对比

Figure 11. Comparison of COMSOL simulation and theoretical calculation results

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图 12 不同单胞数量下的位移传输损失曲线

Figure 12. Displacement transmission loss curves for different cell numbers

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表 1 声子晶体梁的材料和几何性质

Table 1. Material and geometric properties of phonon crystal beams

parameter	BaTiO₃	SrTiO₃
relative permittivity (a)	4×10³	3×10²
ρ/(kg/m³)	4.50×10³	4.81×10³
f/(C/m)	5.0×10^－4	1.0×10^－4
E/(N/m²)	1.62×10¹¹	3.50×10¹¹
b/m	1×10^－10	1×10^－10

下载: 导出CSV

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