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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

梁斌斌 张龙 王炳雷 周慎杰

梁斌斌, 张龙, 王炳雷, 周慎杰. 拟弧长延拓法在静电激励MEMS吸合特性研究中的应用[J]. 应用数学和力学, 2015, 36(4): 386-392. doi: 10.3879/j.issn.1000-0887.2015.04.006
引用本文: 梁斌斌, 张龙, 王炳雷, 周慎杰. 拟弧长延拓法在静电激励MEMS吸合特性研究中的应用[J]. 应用数学和力学, 2015, 36(4): 386-392. doi: 10.3879/j.issn.1000-0887.2015.04.006
LIANG Bin-bin, ZHANG Long, WANG Bing-lei, ZHOU Shen-jie. Application of the PseudoArclength Continuation Algorithm to Investigate the SizeDependent Pull-in Instability of the Electrostatically Actuated MEMS[J]. Applied Mathematics and Mechanics, 2015, 36(4): 386-392. doi: 10.3879/j.issn.1000-0887.2015.04.006
Citation: LIANG Bin-bin, ZHANG Long, WANG Bing-lei, ZHOU Shen-jie. Application of the PseudoArclength Continuation Algorithm to Investigate the SizeDependent Pull-in Instability of the Electrostatically Actuated MEMS[J]. Applied Mathematics and Mechanics, 2015, 36(4): 386-392. 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
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

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

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

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