拟弧长延拓法在静电激励MEMS吸合特性研究中的应用

梁斌斌; 张龙; 王炳雷; 周慎杰

doi:10.3879/j.issn.1000-0887.2015.04.006

拟弧长延拓法在静电激励MEMS吸合特性研究中的应用

doi: 10.3879/j.issn.1000-0887.2015.04.006

¹山东大学工程力学系,济南 250061;²机械结构强度与振动国家重点实验室(西安交通大学),西安 710049;³山东大学机械工程学院,济南 250061

基金项目: 国家自然基金 (11202117；11272186)；山东省自然基金(ZR2012AM014；BS2012ZZ006)

详细信息

作者简介:
梁斌斌（1991—），男，贵州遵义人，硕士生(E-mail: binliang_100@163.com)；王炳雷（1980—），男，山东泰安人，讲师，博士，硕士生导师(通讯作者. E-mail: bwang@sdu.edu.cn).

中图分类号: O302
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出版历程
- 收稿日期: 2014-10-30
- 修回日期: 2014-12-18
- 刊出日期: 2015-04-15

Application of the PseudoArclength Continuation Algorithm to Investigate the SizeDependent Pull-in Instability of the Electrostatically Actuated MEMS

¹Department of Engineering Mechanics, Shandong University, Jinan 250061, P.R.China;²State Key Laboratory for Strength and Vibration of Mechanical Structures(Xi’an Jiaotong University), Xi’an 710049, P.R.China;³School of Mechanical Engineering, Shandong University, Jinan 250061, P.R.China

Funds: The National Natural Science Foundation of China(11202117; 11272186)

摘要

摘要: 在静电激励微机电系统MEMS(micro-electro-mechanical systems)吸合特性研究中，基于应变梯度理论的微梁结构的控制方程是非线性高阶微分方程，给方程的求解带来了困难.由于该问题的数学模型本质上是分叉问题，方程的解支上出现奇异点，而运用局部延拓法无法通过奇异点.因此，通过运用广义微分求积法将控制方程降阶离散，结合拟弧长延拓法使迭代顺利通过奇异点，求出了整个解曲线.结果表明，拟弧长延拓法能有效并准确地求解具有分叉现象的高阶微分方程问题，为精确预测静电激励MEMS的吸合电压提供有力帮助.
- MEMS /
- 吸合特性 /
- 奇异点 /
- 拟弧长延拓法
Abstract: In the study of the electrostatically actuated MEMS (microelectromechanical systems), based on the strain gradient elasticity theory, the governing equations for the microbeam are nonlinear differential equations that are difficult to solve. The mathematical model for this problem is of essential bifurcation, and the solution branches of the equations have inflection points. The iteration process can’t go through the inflection points with the local continuation method. Therefore, the generalized differential quadrature method was applied to discretize and reduce the order of the governing equations, and the pseudoarclength continuation algorithm was used to enable the iteration process to go smoothly through the inflection points, with the complete solution curve calculated. The numerical results show that the pseudoarclength continuation algorithm makes an effective way precisely solving the nonlinear highorder differential equations with bifurcation phenomenon embedded, and helps to accurately predict the pullin voltage of the electrostatically actuated MEMS.
- MEMS /
- pull-in instability /
- inflection point /
- pseudo-arclength continuation algorithm

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参考文献(18)

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拟弧长延拓法在静电激励MEMS吸合特性研究中的应用

doi: 10.3879/j.issn.1000-0887.2015.04.006

作者简介:
梁斌斌（1991—），男，贵州遵义人，硕士生(E-mail: binliang_100@163.com)；王炳雷（1980—），男，山东泰安人，讲师，博士，硕士生导师(通讯作者. E-mail: bwang@sdu.edu.cn).

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Application of the PseudoArclength Continuation Algorithm to Investigate the SizeDependent Pull-in Instability of the Electrostatically Actuated MEMS

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拟弧长延拓法在静电激励MEMS吸合特性研究中的应用

doi: 10.3879/j.issn.1000-0887.2015.04.006

作者简介: 梁斌斌（1991—），男，贵州遵义人，硕士生(E-mail: binliang_100@163.com)；王炳雷（1980—），男，山东泰安人，讲师，博士，硕士生导师(通讯作者. E-mail: bwang@sdu.edu.cn).

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Application of the PseudoArclength Continuation Algorithm to Investigate the SizeDependent Pull-in Instability of the Electrostatically Actuated MEMS

计量

出版历程

目录

作者简介:
梁斌斌（1991—），男，贵州遵义人，硕士生(E-mail: binliang_100@163.com)；王炳雷（1980—），男，山东泰安人，讲师，博士，硕士生导师(通讯作者. E-mail: bwang@sdu.edu.cn).