This paper investigates the voltage–amplitude response of superharmonic resonance of second order (order two) of alternating current (AC) electrostatically actuated microelectromechanical system (MEMS) cantilever resonators. The resonators consist of a cantilever parallel to a ground plate and under voltage that produces hard excitations. AC frequency is near one-fourth of the natural frequency of the cantilever. The electrostatic force includes fringe effect. Two kinds of models, namely reduced-order models (ROMs), and boundary value problem (BVP) model, are developed. Methods used to solve these models are (1) method of multiple scales (MMS) for ROM using one mode of vibration, (2) continuation and bifurcation analysis for ROMs with several modes of vibration, (3) numerical integration for ROM with several modes of vibration, and (4) numerical integration for BVP model. The voltage–amplitude response shows a softening effect and three saddle-node bifurcation points. The first two bifurcation points occur at low voltage and amplitudes of 0.2 and 0.56 of the gap. The third bifurcation point occurs at higher voltage, called pull-in voltage, and amplitude of 0.44 of the gap. Pull-in occurs, (1) for voltage larger than the pull-in voltage regardless of the initial amplitude and (2) for voltage values lower than the pull-in voltage and large initial amplitudes. Pull-in does not occur at relatively small voltages and small initial amplitudes. First two bifurcation points vanish as damping increases. All bifurcation points are shifted to lower voltages as fringe increases. Pull-in voltage is not affected by the damping or detuning frequency.
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March 2019
Research-Article
Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators
Dumitru I. Caruntu,
Dumitru I. Caruntu
Mechanical Engineering Department,
University of Texas Rio Grande Valley,
Edinburg, TX 78539
e-mails: dumitru.caruntu@utrgv.edu;
caruntud2@asme.org;
dcaruntu@yahoo.com
University of Texas Rio Grande Valley,
Edinburg, TX 78539
e-mails: dumitru.caruntu@utrgv.edu;
caruntud2@asme.org;
dcaruntu@yahoo.com
Search for other works by this author on:
Martin A. Botello,
Martin A. Botello
Mechanical Engineering Department,
University of Texas Rio Grande Valley,
Edinburg, TX 78539
University of Texas Rio Grande Valley,
Edinburg, TX 78539
Search for other works by this author on:
Christian A. Reyes,
Christian A. Reyes
Mechanical Engineering Department,
University of Texas Rio Grande Valley,
Edinburg, TX 78539
University of Texas Rio Grande Valley,
Edinburg, TX 78539
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Julio S. Beatriz
Julio S. Beatriz
Mechanical Engineering Department,
University of Texas Rio Grande Valley,
Edinburg, TX 78539
University of Texas Rio Grande Valley,
Edinburg, TX 78539
Search for other works by this author on:
Dumitru I. Caruntu
Mechanical Engineering Department,
University of Texas Rio Grande Valley,
Edinburg, TX 78539
e-mails: dumitru.caruntu@utrgv.edu;
caruntud2@asme.org;
dcaruntu@yahoo.com
University of Texas Rio Grande Valley,
Edinburg, TX 78539
e-mails: dumitru.caruntu@utrgv.edu;
caruntud2@asme.org;
dcaruntu@yahoo.com
Martin A. Botello
Mechanical Engineering Department,
University of Texas Rio Grande Valley,
Edinburg, TX 78539
University of Texas Rio Grande Valley,
Edinburg, TX 78539
Christian A. Reyes
Mechanical Engineering Department,
University of Texas Rio Grande Valley,
Edinburg, TX 78539
University of Texas Rio Grande Valley,
Edinburg, TX 78539
Julio S. Beatriz
Mechanical Engineering Department,
University of Texas Rio Grande Valley,
Edinburg, TX 78539
University of Texas Rio Grande Valley,
Edinburg, TX 78539
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 23, 2018; final manuscript received November 10, 2018; published online January 18, 2019. Assoc. Editor: Eihab Abdel-Rahman.
J. Comput. Nonlinear Dynam. Mar 2019, 14(3): 031005 (8 pages)
Published Online: January 18, 2019
Article history
Received:
March 23, 2018
Revised:
November 10, 2018
Citation
Caruntu, D. I., Botello, M. A., Reyes, C. A., and Beatriz, J. S. (January 18, 2019). "Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators." ASME. J. Comput. Nonlinear Dynam. March 2019; 14(3): 031005. https://doi.org/10.1115/1.4042017
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