Abstract
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.
Highlights
Electrostatically-actuated microbeams have become major components in many micro-electromechanical system (MEMS) devices [1] such as switches [2,3], sensors [4,5] and resonators [6] due to their geometric simplicity, broad applicability and easy to implement characteristics
Since the main objective of this paper is to explore the main resonance problem in the nonlinear dynamics problem, the first-order mode is sufficient to obtain good results
Doubly-clamped electrostatic microresonator considering the effect of surface processing error on the thickness are studied
Summary
Electrostatically-actuated microbeams have become major components in many micro-electromechanical system (MEMS) devices [1] such as switches [2,3], sensors [4,5] and resonators [6] due to their geometric simplicity, broad applicability and easy to implement characteristics. A doubly-clamped beam of variable thickness actuated by a one-sided electrode is considered to study the influence of section variation on static and dynamic behaviors. Results show that the initial offset may induce a complex frequency rebound phenomenon, and there exists the frequency response in the medium and large amplitude in-well transitions between softening and hardening behaviors These two kinds of error forms have a great influence on the mechanical properties of the system, the microbeam model is still an equal section beam. Najar et al [27,44] simulated and analyzed the deflection and motion of variable section beams in MEMS devices, and the effect of changing their geometrical parameters on the static bifurcation and frequency response was observed.
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