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Research Papers

Exploration of New Concepts for Mass Detection in Electrostatically-Actuated Structures Based on Nonlinear Phenomena

[+] Author and Article Information
Mohammad I. Younis

Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902myounis@binghamton.edu

Fadi Alsaleem

Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY 13902

J. Comput. Nonlinear Dynam 4(2), 021010 (Mar 10, 2009) (15 pages) doi:10.1115/1.3079785 History: Received January 08, 2008; Revised July 09, 2008; Published March 10, 2009

This study presents an effort to explore the exploitation of dynamic instabilities and bifurcations in micro-electro-mechanical systems to realize novel methods and functionalities for mass sensing and detection. These instabilities are induced by exciting a microstructure with a nonlinear forcing composed of a dc parallel-plate electrostatic load and an ac harmonic load. The frequency of the ac load is tuned to be near the fundamental natural frequency of the structure (primary resonance) or its multiples (subharmonic resonance). For each excitation method, local bifurcations, such as saddle-node and pitchfork, and global bifurcations, such as the escape phenomenon, may occur. This work aims to explore the utilization of these bifurcations to design novel mass sensors and switches of improved characteristics. One explored concept of a device is a switch triggered by mass threshold. The basic idea of this device is based on the phenomenon of escape from a potential well. This device has the potential of serving as a smart switch that combines the functions of two devices: a sensitive gas/mass sensor and an electromechanical switch. The switch can send a strong electrical signal as a sign of mass detection, which can be used to actuate an alarming system or to activate a defensive or a security system. A second type of explored devices is a mass sensor of amplified response. The basic principle of this device is based on the jump phenomena encountered in pitchfork bifurcations during mass detection. This leads to an amplified response of the excited structure making the sensor more sensitive and its signal easier to be measured. As case studies, these device concepts are first demonstrated by simulations on clamped-clamped and cantilever microbeams. Results are presented using long-time integration for the equations of motion of a reduced-order model. An experimental case study of a capacitive sensor is presented illustrating the proposed concepts. It is concluded that exciting a microstructure at twice its fundamental natural frequency produces the most promising results for mass sensing and detection.

Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic showing the parallel-plate dc electrostatic actuation and the pull-in instability (a) VDC=0, (b) below pull in, (c) pull-in

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Figure 2

The total potential energy (electrostatic+stiffness) and the corresponding phase portrait for a parallel-plate capacitor for the case of a voltage load below pull-in (a) and above pull-in (b)

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Figure 3

A MEMS parallel-plate capacitor showing a dynamic ac+dc actuation

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Figure 4

(a) Frequency-response curves of a clamped-clamped microbeam excited near its first natural frequency for various values of ac loads. (b) For the case of Vac=0.5 V showing the escape-to-pull-in frequency band.

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Figure 5

Dimensional frequency-response curves for the clamped-clamped microbeam of Fig. 4 before and after 5% mass increase. Also shown are two time-history simulations for the response of the microbeam before and after mass detection when excited at a fixed frequency equal to 52 kHz.

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Figure 6

Frequency response of the electrically actuated cantilever microbeams showing superharmonic, primary, and subharmonic resonances. An escape band of frequency is shown near primary resonance.

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Figure 7

Frequency response of the cantilever microbeams of Fig. 6 near primary resonance illustrating the concept of STMT. The dashed line to the left represents the operating point of the microbeam before the mass detection. The dashed line to the right represents the operating point of the microbeam after detecting an analyte, which increases its mass by 3%. The upper figures show the time history of the microbeam response before and after the mass detection. The time t is normalized to t̃=0.04 ms.

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Figure 8

Frequency-response curves for a cantilever microbeam excited at primary resonance illustrating the influence of changing the quality factor Q and ac amplitude Vac. (a) Vac=0.1 V, (b) Q=10.

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Figure 9

Bifurcation diagram showing several scenarios for the dynamical state of a spring-mass-damper system with quadratic stiffness nonlinearity (47)

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Figure 10

The instability tongue of an electrically actuated cantilever beam illustrating the idea of the STMT based on primary resonance excitation

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Figure 11

The operating principle of the STMT and MSAR for the case of subharmonic resonance excitation of a cantilever microbeam. The microbeam is biased by a dc voltage equal to 0.4 V and its quality factor is equal to 100. (a) Vac=0.1 V, (b) Vac=0.2 V.

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Figure 12

Frequency-response curves for a cantilever microbeam excited at subharmonic resonance illustrating the influence of the quality factor Q and ac amplitude Vac. (a) Vac=0.1 V, (b) Q=100.

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Figure 13

The Q-Vac curve showing the subharmonic resonance activation zone for a cantilever beam. For any point of Q and Vac above the curve, subharmonic resonance is activated.

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Figure 14

Frequency-response curves for a cantilever microbeam excited at subharmonic resonance for the case of Q=5 and Vac=0.7 V

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Figure 15

Frequency-response curves showing subharmonic resonances of a clamped-clamped microbeam for various Vac. (a) demonstrates MSAR idea based on subharmonic resonance. (b) indicates a wide escape band of frequencies developed at higher Vac. (a) Vac=0.6 V, (b) Vdc=1.5 V.

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Figure 16

Frequency-response curve and time histories of a clamped-clamped microbeam excited at subharmonic resonance illustrating its utilization for STMT and MSAR at the same time. The first dashed line to the left indicates the original operating point and the other dashed lines indicate the new operating points upon mass detection.

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Figure 17

(a) Frequency-response curves for a clamped-clamped microbeam excited at subharmonic resonance illustrating the influence of the quality ac amplitude Vac. (b) A zoomed view of (a).

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Figure 18

The operating principle of STMT for the case of subharmonic excitation of a clamped-clamped microbeam. The dashed line to the left represents the operating point of the microbeam before the mass detection. The dashed line to the right represents the operating point of the microbeam after detecting an analyte, which increases its mass by 0.18%. The upper figures show the time history of the response before and after the mass detection. The time t is normalized to T=0.07 ms.

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Figure 19

(a) A picture for the tested capacitive sensor (taken apart) and (b) the experimental setup used for testing the capacitive accelerometers under reduced pressure

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Figure 20

The static deflection of the proof mass for different values of Vdc. Shown in the figure are the experimental measurements and the simulated static deflection using a spring-mass model.

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Figure 21

A frequency sweep response for Vdc=40.1 V and Vac=18.4 V with the pressure=150 mtorr. A sampling rate of 0.25 Hz/s was used in this experiment.

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Figure 22

Experiment (forward sweep) versus simulation results of the frequency response of the device when Vdc=40.1 V and Vac=18.4 V.

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Figure 23

Experiment (backward and forward sweeps) versus simulation results for the frequency response of the device around primary resonance

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Figure 24

A picture showing the capacitive sensor with the added mass on top of the proof mass of the device

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Figure 25

The capacitive accelerometer frequency response when excited near primary resonance before and after adding the mass. (a) Small linear response, (b) large response with pull-in gap.

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Figure 26

The capacitive accelerometer frequency response when excited near subharmonic resonance (twice the natural frequency) before and after adding the mass. (a) Small response, (b) large response.

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