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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)

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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"

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