Research Papers

Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators

[+] Author and Article Information
Dumitru I. Caruntu

Mechanical Engineering Department,
University of Texas Rio Grande Valley,
Edinburg, TX 78539
e-mails: dumitru.caruntu@utrgv.edu;

Martin A. Botello, Christian A. Reyes, Julio S. Beatriz

Mechanical Engineering Department,
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 14(3), 031005 (Jan 18, 2019) (8 pages) Paper No: CND-18-1119; doi: 10.1115/1.4042017 History: Received March 23, 2018; Revised November 10, 2018

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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Grahic Jump Location
Fig. 1

Uniform cantilever MEMS resonator of constant thickness t and constant width W, and under electrostatic actuation due to AC voltage V0cosΩt

Grahic Jump Location
Fig. 2

Voltage–amplitude response using MMS, 5T AUTO, and 5T TR; b*=0.01, f=0.26, σ=−0.025

Grahic Jump Location
Fig. 3

Time responses using five term ROM (5T TR); σ=−0.025, U0=0, b*=0.01, f=0.26, (a) δ = 0.4, (b) δ = 0.5, (c) δ = 0.8, and (d) δ = 1.2

Grahic Jump Location
Fig. 4

Time responses using five term ROM (5T TR); σ=−0.025, U0=0.4, b*=0.01, f=0.26, (a) δ = 0.4, (b) δ = 0.5, (c) δ = 1.0, and (d) δ = 1.6

Grahic Jump Location
Fig. 5

Time responses using five term ROM (5T TR); σ=−0.025, U0=0.7, b*=0.01, f=0.26, (a) δ = 0.3, (b) δ = 0.4, (c) δ = 1.0, and (d) δ = 1.2

Grahic Jump Location
Fig. 6

Time responses using five term ROM (5T TR); σ=−0.025, U0=0.95, b*=0.01, f=0.26, (a) δ = 0.2, (b) δ = 0.3, (c) δ = 0.8, and (d) δ = 1.6

Grahic Jump Location
Fig. 7

Time responses using BVP4C with timestep = 0.0005; δ=1.0b*=0.01, f=0.26, σ=−0.025, (a) U0=0, (b) U0=0.4, (c) U0=0.6, and (d) U0=0.8

Grahic Jump Location
Fig. 8

Convergence of voltage–amplitude response using two, three, four, and five term ROM; MMS is included; b*=0.01, f=0.26, σ=−0.025

Grahic Jump Location
Fig. 9

Effect of damping parameter b* on the voltage–amplitude response using MMS and 5T AUTO; f=0.26, σ=−0.025

Grahic Jump Location
Fig. 10

Effect of fringe parameter f on the voltage–amplitude response using MMS and 5T AUTO; b*=0.01, σ=−0.025

Grahic Jump Location
Fig. 11

Effect of detuning frequency σ on the voltage–amplitude response using MMS and 5T AUTO; b*=0.01, f=0.26



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