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； 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)；沈承(1986—)，男，副教授，博士，硕士生导师(通讯作者. E-mail: cshen@nuaa.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
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- 文章访问数: 15
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- 被引次数: 0
出版历程
- 收稿日期: 2025-01-07
- 修回日期: 2025-02-15
- 网络出版日期: 2025-09-10

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

Funds:

The National Science Foundation of China(12202183； 12472089)

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

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