Qualitative Identification of the Static Pull-In and Fundamental Frequency of One-Electrode MEMS Resonators
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Tianjin Key Laboratory of High Speed Cutting and Precision Machining, School of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin 300222, China
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School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255049, China
3
Department of Mechanical Engineering, Henan Mechanical and Electrical Vocational College, Henan 451191, China
4
Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, China
*
Authors to whom correspondence should be addressed.
Micromachines 2018, 9(12), 614; https://doi.org/10.3390/mi9120614
Received: 16 October 2018
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Revised: 14 November 2018
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Accepted: 19 November 2018
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Published: 22 November 2018
This paper attempts to qualitatively identify the static pull-in position, pull-in voltage, and fundamental frequency of one-electrode microresonators from a physical perspective. During theoretical derivation, a generalized one-degree-of-freedom (1-DOF) model in nondimensional form derived using the differential quadrature method (DQM) is first introduced and then transformed for frequency normalization. Based on the deduced formulas, the upper and lower bounds of the static pull-in position and pull-in voltage are both deduced through mathematical proof. To distinguish the monotonic and nonmonotonic behavior of the fundamental frequency versus direct current (DC) voltage, a critical condition decided only by cubic stiffness is then determined. For the first time, two extreme static positions, as well as the corresponding fundamental frequencies and DC voltages to identify different frequency behaviors are derived, and their variations versus cubic stiffness are then discussed and verified. During the simulation process, a high-order DQM and COMSOL 2D model are both applied for numerical analyses. Guided by nondimensional results, typical behaviors with specific physical parameters are examined in detail. Results demonstrate that the curve tendencies between all the qualitative results and quantitative numerical simulations in dimensional form agree well with each other, implying the possibility of using 1-DOF model to qualitatively discuss physical parameters effects on the system statics and dynamics.
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Keywords:
MEMS; resonator; one-electrode; static pull-in; fundamental frequency
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MDPI and ACS Style
Han, J.; Li, L.; Jin, G.; Ma, W.; Feng, J.; Jia, H.; Chang, D. Qualitative Identification of the Static Pull-In and Fundamental Frequency of One-Electrode MEMS Resonators. Micromachines 2018, 9, 614. https://doi.org/10.3390/mi9120614
AMA Style
Han J, Li L, Jin G, Ma W, Feng J, Jia H, Chang D. Qualitative Identification of the Static Pull-In and Fundamental Frequency of One-Electrode MEMS Resonators. Micromachines. 2018; 9(12):614. https://doi.org/10.3390/mi9120614
Chicago/Turabian StyleHan, Jianxin, Lei Li, Gang Jin, Wenkui Ma, Jingjing Feng, Haili Jia, and Dongmei Chang. 2018. "Qualitative Identification of the Static Pull-In and Fundamental Frequency of One-Electrode MEMS Resonators" Micromachines 9, no. 12: 614. https://doi.org/10.3390/mi9120614
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