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

LIANG Bin-bin; ZHANG Long; WANG Bing-lei; ZHOU Shen-jie

doi:10.3879/j.issn.1000-0887.2015.04.006

Volume 36 Issue 4

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Article Navigation > Applied Mathematics and Mechanics > 2015 > 36(4): 386-392

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

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

doi: 10.3879/j.issn.1000-0887.2015.04.006

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)

Received Date: 2014-10-30
Rev Recd Date: 2014-12-18
Publish Date: 2015-04-15

Abstract

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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References(18)

References

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