Technology Reviews

Nonlinear Dynamics and Its Applications in Micro- and Nanoresonators

[+] Author and Article Information
Jeffrey F. Rhoads1

School of Mechanical Engineering, Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907jfrhoads@purdue.edu

Steven W. Shaw

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824shawsw@msu.edu

Kimberly L. Turner

Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106turner@engineering.ucsb.edu


Corresponding author.

J. Dyn. Sys., Meas., Control 132(3), 034001 (Apr 16, 2010) (14 pages) doi:10.1115/1.4001333 History: Received January 19, 2009; Revised February 10, 2010; Published April 16, 2010; Online April 16, 2010

This review provides a summary of work on the resonant nonlinear dynamics of micro- and nanoelectromechanical systems. This research area, which has been active for approximately a decade, involves the study of nonlinear behaviors arising in small scale, vibratory, mechanical devices that are typically integrated with electronics for use in signal processing, actuation, and sensing applications. The inherent nature of these devices, which includes low damping, desired resonant operation, and the presence of nonlinear potential fields, sets an ideal stage for the appearance of nonlinear behavior. While nonlinearities are typically avoided in device design, they have the potential to allow designers to beneficially leverage nonlinear behavior in certain applications. This paper provides an overview of the fundamental research on nonlinear behaviors arising in micro-/nanoresonators, including direct and parametric resonances in individual resonators and coupled resonator arrays, and also describes the active exploitation of nonlinear dynamics in the development of resonant mass sensors, inertial sensors, and electromechanical signal processing systems. This paper closes with some brief remarks about important ongoing developments in the field.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

A schematic of the representative, electrostatically-actuated micro/nanoresonator discussed in Sec. 2

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Figure 2

(a) An interdigitated electrostatic comb drive. (b) A noninterdigitated electrostatic comb drive. Note that the included arrows indicate the direction of dominant motion for the moveable part of the device. The other banks of comb fingers are fixed (picture courtesy of B. DeMartini).

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Figure 3

(a) An electrostatically actuated nanoresonator comprised of a clamped-clamped beam. (b) Nonlinear frequency response obtained from the device. Note that because these responses were obtained solely through up-sweeps in frequency, hysteresis is not evident (pictures courtesy of E. Buks).

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Figure 4

A parametrically excited torsional microresonator driven through the use of noninterdigitated comb drives

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Figure 5

A representative frequency response obtained from an electrostatically actuated, parametrically excited resonator (a planar variant of the device shown in Fig. 4). Note that the mixed response characteristics displayed here are yet to be observed in any macroscale device (adapted from Ref. 121).

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Figure 6

A set of microbeam resonators actuated by Lorentz forces. The light areas on the beam are deposited wires. A periodic current flowing through the wire at the end of the beam creates an alternating axial load when the beam is placed in a transverse magnetic field, thereby producing parametric excitation (from Ref. 135, picture courtesy of K. (Lukes) Moran).

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Figure 7

A 67-element array of electrostatically coupled, fixed-fixed microbeams (adapted from Ref. 161, picture courtesy of E. Buks)




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