考虑表面效应的压电纳米梁的振动研究

周强; 张志纯; 龙志林; 武井祥; 黄彬; 金花

doi:10.21656/1000-0887.400330

考虑表面效应的压电纳米梁的振动研究

doi: 10.21656/1000-0887.400330

¹湘潭大学物理与光电工程学院, 湖南湘潭 411105;²湘潭大学土木工程与力学学院, 湖南湘潭 411105

基金项目: 国家自然科学基金（51471139）

详细信息

作者简介:
周强（1995—），男，硕士生(E-mail: 201721521313@smail.xtu.edu.cn)；张志纯（1965—），男，副教授（通讯作者. E-mail: zhangzhch2188@163.com）；龙志林（1969—），男，教授（E-mail: longzl@xtu.edu.cn）；武井祥（1981—），男，讲师（E-mail: jingxiangwu@xtu.edu.cn）；黄彬（1992—），男，硕士生（E-mail: cqswzqhb@163.com）；金花（1995—），女，硕士生（E-mail: 15707970975@163.com）.

中图分类号: O321
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- 被引次数: 0
出版历程
- 收稿日期: 2019-10-30
- 修回日期: 2019-12-25
- 刊出日期: 2020-08-01

Vibration of Piezoelectric Nanobeams With Surface Effects

¹School of Physics and Optoelectronics, Xiangtan University, Xiangtan, Hunan 411105, P.R.China;²College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, Hunan 411105, P.R.China

Funds: The National Natural Science Foundation of China（51471139）

摘要

摘要: 一维压电纳米材料在微纳米机电系统（MEMS/NEMS）中应用广泛，对其力学性能的有效表征至关重要。基于Gurtin-Murdoch表面理论，建立了一种表征一维纳米材料表面效应的新模型。基于Timoshenko梁理论，建立了考虑表面效应的压电纳米梁控制方程，推导了几种不同边界条件下压电纳米梁的频率方程和振型方程的精确解。提出了一种在有限元软件中实现表面效应模拟的计算方法，在ABAQUS中实现了考虑表面效应的压电纳米梁的数值模拟。理论结果和有限元模拟结果吻合较好，验证了理论模型的正确性和有效性。表面效应对纳米梁振动的频率影响显著，而在某种程度上对振型有一定的影响.
- 纳米线 /
- 表面效应 /
- 压电效应 /
- 自由振动
Abstract: One-dimensional piezoelectric nanomaterials are widely used in MEMS/NEMS systems, and it is important to effectively characterize their mechanical properties. Based on the Gurtin-Murdoch surface theory, a new model for one-dimensional nanomaterials with surface effects was established. Based on the Timoshenko beam theory, the governing equations for piezoelectric nanowires with surface effects were derived, and the exact solutions of frequency equations and mode equations for piezoelectric nanowires under different boundary conditions were obtained. A method to simulate the surface effects with the finite element software was proposed, and the numerical simulation of piezoelectric nanobeams with surface effects was realized in ABAQUS. The theoretical results are in good agreement with the finite element simulation results, which verifies the correctness and validity of the theoretical model. The surface effect was very significant to the vibration frequencies of nanobeams and somewhat influences the mode shapes.
- nanowire /
- surface effect /
- piezoelectric effect /
- free vibration

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