考虑表面应力的微悬臂梁质量传感器的建模与仿真

doi:10.12068/j.issn.1005-3026.2018.02.018

东北大学学报:自然科学版 ›› 2018, Vol. 39 ›› Issue (2): 237-241.DOI: 10.12068/j.issn.1005-3026.2018.02.018

考虑表面应力的微悬臂梁质量传感器的建模与仿真

马树军，修强

(东北大学机械工程与自动化学院，辽宁沈阳110819)

收稿日期:2016-08-11 修回日期:2016-08-11 出版日期:2018-02-15 发布日期:2018-02-09
通讯作者: 马树军
作者简介:马树军(1982-)，男，河北保定人，东北大学副教授，博士.
基金资助:
国家自然科学基金资助项目(51505076)；辽宁省自然科学基金资助项目(2015020105)；中央高校基本科研业务费专项资金资助项目(N140304010，N150308001)；辽宁省高等学校创新团队项目(LT2014006).

Modelling and Simulation of a Surface Stress-Included Microcantilever-based Mass Sensor

MA Shu-jun， XIU Qiang

School of Mechanical Engineering & Automation， Northeastern University， Shenyang 110819， China.

Received:2016-08-11 Revised:2016-08-11 Online:2018-02-15 Published:2018-02-09
Contact: MA Shu-jun
About author:-
Supported by:
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摘要/Abstract

摘要： 为了考虑悬臂梁谐振器表面吸附层或者不同材料涂层引起的表面应力的影响，进而提高质量传感器的精度和性能，基于瑞利-里兹法提出了考虑表面应力的悬臂梁质量传感器的理论方法.在悬臂梁振动的控制方程中引入应力系数对其振型函数进行修正，并系统地分析对悬臂梁振动频率的影响，再根据瑞利法建立微悬臂梁质量传感器的理论模型.应用该方法，纳米颗粒的位置和质量可以通过颗粒吸附前后悬臂梁的频率移动来精确确定.该方法的准确性和可行性通过有限元仿真进行了验证.

关键词: 微悬臂梁, 质量传感, 表面应力, 欧拉-伯努利梁理论, 瑞利-里兹法

Abstract: A theoretical model， which takes surface stress into account by applying Rayleigh-Ritz theorem， for a cantilever-based mass sensor is proposed， in order to consider the surface stress induced by the adsorbed layer or coating of different materials on the cantilever resonator and to further enhance the accuracy and performance of the cantilever sensor. Stress parameter is introduced into the governing equation of the cantilever vibration to adjust the mode shape function， and the influence of the surface stress towards the vibration is systematically analyzed. With this model， the position and mass of the particle can be precisely determined through the frequency shifts of the microcantilever before and after the particle adsorption. The accuracy and the reliability of this method were validated by finite element simulation.

Key words: microcantilever, mass sensing, surface stress, Euler-Bernoulli beam theory, Rayleigh-Ritz theorem

中图分类号:

TP206

马树军，修强. 考虑表面应力的微悬臂梁质量传感器的建模与仿真[J]. 东北大学学报:自然科学版, 2018, 39(2): 237-241.

MA Shu-jun， XIU Qiang. Modelling and Simulation of a Surface Stress-Included Microcantilever-based Mass Sensor[J]. Journal of Northeastern University Natural Science, 2018, 39(2): 237-241.

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考虑表面应力的微悬臂梁质量传感器的建模与仿真

Modelling and Simulation of a Surface Stress-Included Microcantilever-based Mass Sensor

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