您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（工学版）》

山东大学学报 (工学版) ›› 2019, Vol. 49 ›› Issue (6): 107-112.doi: 10.6040/j.issn.1672-3961.0.2019.061

• 机械与能动工程 • 上一篇    下一篇

双层压电微梁固有特性的尺寸依赖性

刘宇(),周慎杰*(),吴康辉   

  1. 山东大学机械工程学院, 山东 济南 250061
  • 收稿日期:2019-02-14 出版日期:2019-12-20 发布日期:2019-12-17
  • 通讯作者: 周慎杰 E-mail:liuyugodlike@126.com;zhousj@sdu.edu.cn
  • 作者简介:刘宇(1992—),男,山西阳泉人,硕士研究生,主要研究方向为压电微构件力电耦合. E-mail:liuyugodlike@126.com
  • 基金资助:
    山东省自然科学基金资助项目(ZR2018MA026)

Size-dependenct intrinsic properties of the bilayer piezoelectric microbeam

Yu LIU(),Shenjie ZHOU*(),Kanghui WU   

  1. School of Mechanical Engineering, Shandong University, Jinan 250061, Shandong, China
  • Received:2019-02-14 Online:2019-12-20 Published:2019-12-17
  • Contact: Shenjie ZHOU E-mail:liuyugodlike@126.com;zhousj@sdu.edu.cn
  • Supported by:
    山东省自然科学基金资助项目(ZR2018MA026)

RichHTML

7

PDF (PC)

294

摘要：

为探究双层压电微梁固有特性随特征尺寸的变化规律,应用含挠曲电效应的压电偶应力理论,建立双层压电微梁动态性能尺寸效应理论模型,求解双层压电微梁的固有频率,通过数值分析讨论微梁无量纲固有频率的尺寸依赖性,研究压电效应和挠曲电效应对微梁无量纲固有频率的影响。数值分析结果表明:双层压电微梁的无量纲固有频率随着梁厚度的减小而增大,呈现出明显的尺寸依赖性;与不计力电耦合效应的结果相比,双层压电微梁无量纲固有频率的尺寸依赖性更为明显,主要是由挠曲电效应引起的,而压电效应的影响很小。

关键词: 双层压电微梁, 固有频率, 尺寸依赖性, 压电效应, 挠曲电效应

Abstract:

A size-dependent dynamic model of a bilayer piezoelectric microbeam was established based on the couple stress piezoelectric theory incorporating flexoelectric effects to explore the variation of the intrinsic properties of the bilayer piezoelectric microbeam with the characteristic size. The natural frequency of the bilayer piezoelectric microbeam was obtained. The influence of piezoelectric effects and flexoelectric effects on the natural frequency of the microbeam was discussed by numerical analysis method. The results indicated that the dimensionless natural frequency of the bilayer piezoelectric microbeam increased significantly as the beam thickness decreased. It was also found that the dimensionless natural frequency of the bilayer piezoelectric microbeam showed stronger size-dependency than that of the model without considering electromechanical coupling effects, which mainly resulted from flexoelectric effects, and piezoelectric effects exerted minor influence on the beam natural frequency.

Key words: bilayer piezoelecteic microbeam, natural frequency, size dependency, piezoelectric effects, flexoelectric effects

中图分类号: 

  • TN384

图1

双层压电微梁示意图"

图2

微梁无量纲固有频率随无量纲厚度的变化规律"

图3

力电耦合效应对微梁固有频率的影响"

图4

转动梯度反对称部分对微梁固有频率的影响"

图5

双层压电微梁固有频率随相对厚度的变化规律"

1 SOHI A N , NIEVA P M . Frequency response of curved bilayer microcantilevers with applications to surface stress measurement[J]. Journal of Applied Physics, 2016, 119 (4): 044503.
doi: 10.1063/1.4940951
2 BEGLEY M R . The impact of materials selection and geometry on multi-functional bilayer micro-sensors and actuators[J]. Journal of Micromechanics and Microengineering, 2005, 15 (12): 2379- 2388.
doi: 10.1088/0960-1317/15/12/021
3 DING G , ZHANG Y , YANG C , et al. Electrochemical microactuator based on hydrogen-absorbing film: the principle and first results[J]. Proc Spie, 2001, 104 (10): 312- 317.
4 韦笑梅, 黄银燕. 智能梁振动分析的修正Fourier级数方法[J]. 广西工学院学报(自然科学版), 2010, 21 (4): 75- 80.
WEI Xiaomei , HUANG Yinyan . Vibration analysis of a smart beam via modified Fourier series[J]. Journal of Guangxi University of Technology(Natural Science), 2010, 21 (4): 75- 80.
5 林晓辉, 苏雅璇, 周志东, 等. 电学开路挠曲电悬臂梁自振频率分析[J]. 力学季刊, 2018, 39 (2): 383- 394.
LIN Xiaohui , SU Yaxuan , ZHOU Zhidong , et al. Analysis of the natural frequency for flexoelectric cantilever beams under the open-circuit condition[J]. Chinese Quarterly of Mechanics, 2018, 39 (2): 383- 394.
6 ZUKBO P , CATALAN G , TAGANTSEV AK . Flexoelectric effect in solids[J]. Annual Review of Materials Research, 2013, 43 (1): 387- 421.
doi: 10.1146/annurev-matsci-071312-121634
7 YUDIN PV , TAGANTSEV AK . Fundamentals of flexoelectricity in solids[J]. Nanotechnology, 2013, 24 (43): 432001.
doi: 10.1088/0957-4484/24/43/432001
8 XINGJIA L , YING L . Flexoelectric effect on vibration of piezoelectric microbeams based on a modified couple stress theory[J]. Shock and Vibration, 2017, 2017, 1- 7.
9 WANG G F , YU S W , FENG X Q . A piezoelectric constitutive theory with rotation gradient effects[J]. European Journal of Mechanics, 2004, 23 (3): 455- 466.
doi: 10.1016/j.euromechsol.2003.12.005
10 HADJESFANDIARI A R . Size-dependent piezoelectricity[J]. International Journal of Solids and Structures, 2013, 50 (18): 2781- 2791.
doi: 10.1016/j.ijsolstr.2013.04.020
11 LI Anqing , ZHOU Shenjie , QI Lu , et al. A flexoelectric theory with rotation gradient effects for elastic dielectrics[J]. Modelling and Simulation in Materials Science and Engineering, 2016, 24 (1): 015009.
doi: 10.1088/0965-0393/24/1/015009
12 吴康辉.含挠曲电效应的横观各向同性压电材料偶应力理论[D].济南:山东大学机械工程学院, 2018.
WU Kanghui. A couple stress theory including flexoelectric effects for transversely isotropic piezoelectric materials[D]. Jinan: School of Mechanical Engineering, Shandong University, 2018.
13 YAN Z , JJIANG L Y . Flexoelectric effect on the electroelastic responses of bending piezoelectric nanobeams[J]. Journal of Applied Physics, 2013, 113 (19): 194102.
doi: 10.1063/1.4804949
14 SAHMANI S , BAHRAMI M . Size-dependent dynamic stability analysis of microbeams actuated by piezoelectric voltage based on strain gradient elasticity theory[J]. Journal of Mechanical Science and Technology, 2015, 29 (1): 325- 333.
doi: 10.1007/s12206-014-1239-3
15 LI Z , WANG H , ZHENG S . Bending and free vibration of functionally graded piezoelectric microbeams based on the modified couple stress theory[J]. Annals of Solid and Structural Mechanics, 2018, 10 (1): 1- 16.
16 BENI T , YAGHOUB . Size-dependent analysis of piezoelectric nanobeams including electro-mechanical coupling[J]. Mechanics Research Communications, 2016, 75, 67- 80.
doi: 10.1016/j.mechrescom.2016.05.011
17 ZHENG Y , CHEN T , CHEN C . A size-dependent model to study nonlinear static behavior of piezoelectric cantilever microbeams with damage[J]. Microsystem Technologies, 2017, 23 (10): 4679- 4686.
doi: 10.1007/s00542-016-3246-z
18 TOUPIN R A . Elastic materials with couple-stresses[J]. Archive for Rational Mechanics & Analysis, 1962, 11 (1): 385- 414.
19 李安庆, 周慎杰, 周莎莎. 双层微梁固有特性的尺寸效应[J]. 工程力学, 2014, 31 (7): 223- 228.
LI Anqing , ZHOU Shenjie , ZHOU Shasha . The size-dependent inherent property of bilayered micro-beams[J]. Engineering Mechanics, 2014, 31 (7): 223- 228.
20 DENG Q . Size-dependent flexoelectric response of a truncated cone and the consequent ramifications for the experimental measurement of flexoelectric properties[J]. Journal of Applied Mechanics, 2017, 84 (10): 101007.
doi: 10.1115/1.4037552
21 MARANGANTI R , SHARMA P . Atomistic determination of flexoelectric properties of crystalline dielectrics[J]. Physical Review B, 2009, 80 (5): 1956- 1960.
[1] 魏守水,江兴娥,白光磊,姜春香 . 直管形行波微流体驱动模型的模态与谐响应分析[J]. 山东大学学报(工学版), 2006, 36(6): 67-70 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 王素玉,艾兴,赵军,李作丽,刘增文 . 高速立铣3Cr2Mo模具钢切削力建模及预测[J]. 山东大学学报(工学版), 2006, 36(1): 1 -5 .
[2] 余嘉元1 , 田金亭1 , 朱强忠2 . 计算智能在心理学中的应用[J]. 山东大学学报(工学版), 2009, 39(1): 1 -5 .
[3] 陈瑞,李红伟,田靖. 磁极数对径向磁轴承承载力的影响[J]. 山东大学学报(工学版), 2018, 48(2): 81 -85 .
[4] 于海波,李宇,余恬,雷虹 . W波段折叠波导慢波系统的尺寸对其冷特性的影响[J]. 山东大学学报(工学版), 2008, 38(3): 90 -94 .
[5] 赵勇 田四明 曹哲明. 宜万铁路复杂岩溶隧道施工地质工作方法[J]. 山东大学学报(工学版), 2009, 39(5): 91 -95 .
[6] 孙宗耀,刘允刚 . 一类2维不确定非线性系统自适应输出反馈镇定[J]. 山东大学学报(工学版), 2007, 37(5): 34 -39 .
[7] 孟健, 李贻斌, 李彬. 四足机器人跳跃步态控制方法[J]. 山东大学学报(工学版), 2015, 45(3): 28 -34 .
[8] 郑洪亮,孔凡利, , 田学雷 . Al-Cu合金成分变化对其凝固潜热影响的研究[J]. 山东大学学报(工学版), 2008, 38(2): 10 -12 .
[9] 董彤 袁淑娟 葛军饴 洪芳 郁黎明 曹世勋 张金仓. 磁制冷材料Gd5Ge4中的磁玻璃态[J]. 山东大学学报(工学版), 2009, 39(3): 67 -70 .
[10] 郝明辉,王锡平,王敏,周慎杰 .

考虑偶应力影响的有限大板单边裂纹计算

[J]. 山东大学学报(工学版), 2008, 38(2): 92 -95 .
版权所有 © 2018 《山东大学学报(工学版)》编辑部　
地址: 济南市山大南路27号（250100）　 电话: 0531-88366735　 E-mail: xbgxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发