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Static and Dynamic Mechanical Behaviors of Electrostatic MEMS Resonator with Surface Processing Error

1,2,3,*, 1,3, 2,* and 1,3,*
Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin 300384, China
Beijing Key Laboratory on Nonlinear Vibrations and Strength of Mechanical Structures, Beijing University of Technology, College of Mechanical Engineering, Beijing 100124, China
National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin 300384, China
Authors to whom correspondence should be addressed.
Micromachines 2018, 9(1), 34;
Received: 30 November 2017 / Revised: 31 December 2017 / Accepted: 12 January 2018 / Published: 17 January 2018
(This article belongs to the Special Issue Micro-Resonators: The Quest for Superior Performance)
PDF [12017 KB, uploaded 18 January 2018]


The micro-electro-mechanical system (MEMS) resonator developed based on surface processing technology usually changes the section shape either due to excessive etching or insufficient etching. In this paper, a section parameter is proposed to describe the microbeam changes in the upper and lower sections. The effect of section change on the mechanical properties is studied analytically and verified through numerical and finite element solutions. A doubly-clamped microbeam-based resonator, which is actuated by an electrode on one side, is investigated. The higher-order model is derived without neglecting the effects of neutral plane stretching and electrostatic nonlinearity. Further, the Galerkin method and Newton–Cotes method are used to reduce the complexity and order of the derived model. First of all, the influence of microbeam shape and gap variation on the static pull-in are studied. Then, the dynamic analysis of the system is investigated. The method of multiple scales (MMS) is applied to determine the response of the system for small amplitude vibrations. The relationship between the microbeam shape and the frequency response is discussed. Results show that the change of section and gap distance can make the vibration soften, harden, and so on. Furthermore, when the amplitude of vibration is large, the frequency response softening effect is weakened by the MMS. If the nonlinearity shows hardening-type behavior at the beginning, with the increase of the amplitude, the frequency response will shift from hardening to softening behavior. The large amplitude in-well motions are studied to investigate the transitions between hardening and softening behaviors. Finally, the finite element analysis using COMSOL software (COMSOL Inc., Stockholm, Sweden) is carried out to verify the theoretical results, and the two results are very close to each other in the stable region. View Full-Text
Keywords: MEMS; processing error; section parameter; nonlinear vibration MEMS; processing error; section parameter; nonlinear vibration

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Feng, J.; Liu, C.; Zhang, W.; Hao, S. Static and Dynamic Mechanical Behaviors of Electrostatic MEMS Resonator with Surface Processing Error. Micromachines 2018, 9, 34.

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