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Research Papers

Microelectromechanical Systems Cantilever Resonators Under Soft Alternating Current Voltage of Frequency Near Natural Frequency

[+] Author and Article Information
Dumitru I. Caruntu

Mem. ASME
Mechanical Engineering Department,
University of Texas Pan American,
1201 W University Drive,
Edinburg, TX 78539
e-mail: caruntud@utpa.edu

Martin W. Knecht

Engineering Department,
South Texas College,
McAllen, TX 78501
e-mail: mknecht@southtexascollege.edu

1University of Texas Pan American becomes University of Texas Rio Grande Valley starting Fall 2015, e-mail: caruntud2@asme.org; dcaruntu@yahoo.com.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 6, 2012; final manuscript received August 16, 2014; published online January 9, 2015. Assoc. Editor: Qingze Zou.

J. Dyn. Sys., Meas., Control 137(4), 041016 (Apr 01, 2015) (8 pages) Paper No: DS-12-1363; doi: 10.1115/1.4028887 History: Received November 06, 2012; Revised August 16, 2014; Online January 09, 2015

This paper deals with nonlinear-parametric frequency response of alternating current (AC) near natural frequency electrostatically actuated microelectromechanical systems (MEMS) cantilever resonators. The model includes fringe and Casimir effects, and damping. Method of multiple scales (MMS) and reduced order model (ROM) method are used to investigate the case of weak nonlinearities. It is reported for uniform resonators: (1) an excellent agreement between the two methods for amplitudes less than half of the gap, (2) a significant influence of fringe effect and damping on bifurcation frequencies and phase–frequency response, respectively, (3) an increase of nonzero amplitudes' frequency range with voltage increase and damping decrease, and (4) a negligible Casimir effect at microscale.

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Figures

Grahic Jump Location
Fig. 1

Uniform MEMS cantilever resonator

Grahic Jump Location
Fig. 2

Influence of scaling on dimensionless parameters α and δ with respect to the gap g

Grahic Jump Location
Fig. 6

Influence of the fringe correction f on the frequency response. The parameters used are α = 0, δ = 0.1, and b* = 0.01. (a) Amplitude–frequency response using MMS, (b) phase–amplitude response using MMS, and (c) time response using ROM for σ = -0.013 and initial tip displacement is U0 = 0; as the fringe correction parameter increases, the steady-state amplitude increases

Grahic Jump Location
Fig. 4

Influence of the dimensionless damping parameter b* on the frequency response. The parameters used are α = 0, δ = 0.1, and f = 0.26. (a) Amplitude–frequency response using MMS, (b) Phase–frequency response using MMS, and (c) time response using ROM for σ = -0.013 and initial amplitude U0 = 0.

Grahic Jump Location
Fig. 5

Influence of the dimensionless excitation parameter δ on the frequency response. The parameters used are α = 0, f = 0.26, and b* = 0.01. (a) Amplitude–frequency response using MMS, (b) phase–frequency response using MMS, and (c) time response using ROM for σ = -0.015 and initial amplitude U0 = 0.2; as the excitation increases, the steady-state amplitude increases.

Grahic Jump Location
Fig. 3

Frequency response of the uniform MEMS resonator for AC near first natural frequency using MMS and ROM. The solid and dashed lines are solutions from the MMS representing stable and unstable points, respectively. Parameters values used are α = 0, δ = 0.1, f = 0.26, and b* = 0.01. (a) Amplitude–frequency response using MMS and ROM. The points showed are steady-states using ROM, two terms (diamonds), three terms (circles), four terms (triangles), and five terms (squares). A and B are points where pull-in is predicted using the four and five term ROMs. C is the bifurcation point of the supercritical Hopf bifurcation. (b) Phase–frequency response using MMS, and (c) time response of the tip of a uniform cantilevered resonator for σ = -0.015 using the five term ROM method.

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