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Nonlinear Behavior of Electrostatically Actuated Microbeams with Coupled Longitudinal–Transversal Vibration

School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255000, China
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Micromachines 2019, 10(5), 315; https://doi.org/10.3390/mi10050315
Received: 3 April 2019 / Revised: 30 April 2019 / Accepted: 6 May 2019 / Published: 10 May 2019
(This article belongs to the Section A:Physics)
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Abstract

Microelectromechanical switch has become an essential component in a wide variety of applications, ranging from biomechanics and aerospace engineering to consumer electronics. Electrostatically actuated microbeams and microplates are chief parts of many MEMS instruments. In this study, the nonlinear characteristics of coupled longitudinal–transversal vibration are analyzed, while an electrostatically actuated microbeam is designed considering that the frequency ratio is two to one between the first longitudinal vibration and transversal vibration. The nonlinear governing equations are truncated into a set of coupled ordinary differential equations by the Galerkin method. Then the equations are solved using the multiple-scales method and the nonlinear dynamics of the internal resonance is investigated. The influence of bias voltage, longitudinal excitation and frequency detuning parameters are mainly analyzed. Results show that using the pseudo-arclength continuation method, the nonlinear amplitude–response curves can be plotted continuously. The saturation and jump phenomena are greatly affected by the bias voltage and the detuning frequency. Beyond the critical excitation amplitude, the response energy will transfer from the longitudinal motion to the transversal motion, even the excitation is employed on the longitudinal direction. The large-amplitude jump of the low-order vibration mode can be used to detect the variation of the conditions or parameters, which shows great potential in improving precision of MEMS switches. View Full-Text
Keywords: electrostatically actuated microbeam; coupled longitudinal–transversal vibration; pseudo-arclength continuation method; multiple-scales method electrostatically actuated microbeam; coupled longitudinal–transversal vibration; pseudo-arclength continuation method; multiple-scales method
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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MDPI and ACS Style

Ma, C.; Cao, L.; Li, L.; Shao, M.; Jing, D.; Guo, Z. Nonlinear Behavior of Electrostatically Actuated Microbeams with Coupled Longitudinal–Transversal Vibration. Micromachines 2019, 10, 315.

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