曹天捷. 温度变化对受静电力作用微圆板的影响分析[J]. 工程力学, 2015, 32(2): 20-30. DOI: 10.6052/j.issn.1000-4750.2013.09.0806
引用本文: 曹天捷. 温度变化对受静电力作用微圆板的影响分析[J]. 工程力学, 2015, 32(2): 20-30. DOI: 10.6052/j.issn.1000-4750.2013.09.0806
CAO Tian-jie. ANALYSIS OF TEMPERATUIRE CHANGE EFFECT ON ELECTROSTATICALLY ACTUATED CLAMPED CIRCULAR MICRO-PLATES[J]. Engineering Mechanics, 2015, 32(2): 20-30. DOI: 10.6052/j.issn.1000-4750.2013.09.0806
Citation: CAO Tian-jie. ANALYSIS OF TEMPERATUIRE CHANGE EFFECT ON ELECTROSTATICALLY ACTUATED CLAMPED CIRCULAR MICRO-PLATES[J]. Engineering Mechanics, 2015, 32(2): 20-30. DOI: 10.6052/j.issn.1000-4750.2013.09.0806

温度变化对受静电力作用微圆板的影响分析

ANALYSIS OF TEMPERATUIRE CHANGE EFFECT ON ELECTROSTATICALLY ACTUATED CLAMPED CIRCULAR MICRO-PLATES

  • 摘要: 以考虑温度效应时,受静电力作用的微圆板静力弯曲变形微分方程为基础,该文首先针对轴对称问题的特点,利用级数展开和求极限法则,对圆板静力弯曲变形微分方程进行了改进。改进后的微分方程消除了圆心处的奇异性。其次,利用改进后的圆板静力变形弯曲微分方程,对周边固支圆板受静电力和温度变化作用下的受力变形进行分析。分析过程分为3个阶段:正常模式、过渡模式和接触模式。在数值求解圆板弯曲变形微分方程时,主要将非线性微分方程的求解化成迭代求解两个未知量的问题,一个未知量是形成静电场力的电压,而另一个未知量是圆板的一个边界条件。在实例中,给出了部分计算结果,包括:温度变化对不同阶段圆板受力变形的影响,温度变化对吸合电压的影响,以及不同温度变化下,圆板的几何尺寸对吸合电压的影响,从而可以更好地了解温度变化的作用和影响。

     

    Abstract: Based on the differential governing equation of electrostatically actuated clamped circular micro-plates with temperature changes, Taylor's series expansion and limit analysis are first used to modify the differential governing equation for an axisymmetric solid circular plate. In the modified equation, the singularity at the center of a micro plate does not occur. The modified equation is then employed to analyze the electrostatically actuated clamped circular micro-plate with temperature changes. The analysis for a circular micro-plate is classified into three stages, named a normal mode, a transition mode, and a touch mode. The numerical solution of the differential governing equation for different modes is mainly attributed to solve for an applied voltage and one unknown boundary condition, which could be obtained by using a two-fold method of bisection based on the shooting method. In examples, the entire mechanical behavior of a circular plate over an operational voltage range is investigated and the effects of temperature changes on a pull-in voltage with different dimensions of the plate are studied. The obtained results are useful for understanding the effect of temperature changes on the behavior of a circular plate.

     

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