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The Effects of Initial Rise and Axial Loads on MEMS Arches

[+] Author and Article Information
S. A. Tella, A. Z. Hajjaj

Physical Science and Engineering Division,
King Abdullah University of Science
and Technology,
P. O. Box 4700,
Thuwal 23955-6900, Saudi Arabia

M. I. Younis

Physical Science and Engineering Division,
King Abdullah University of Science
and Technology,
P. O. Box 4700,
Thuwal 23955-6900, Saudi Arabia
e-mail: mohammad.younis@kaust.edu.sa

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 1, 2016; final manuscript received March 19, 2017; published online May 30, 2017. Assoc. Editor: John Judge.

J. Vib. Acoust 139(4), 040905 (May 30, 2017) (8 pages) Paper No: VIB-16-1572; doi: 10.1115/1.4036400 History: Received December 01, 2016; Revised March 19, 2017

Arch microbeams have been utilized and proposed for many uses over the past few years due to their large tunability and bistability. However, recent experimental data have shown different mechanical behaviors of arches when subjected to axial loads, i.e., their stiffness may increase or decrease with applied axial loads. This paper aims to investigate in depth, the influence of the competing effects of initial rise and axial loads on the mechanical behavior of micromachined arches; mainly their static deflection and resonant frequencies. Based on analytical solutions, the static response and eigenvalue problems are analyzed for various values of initial rises and axial loads. Universal curves showing the variation of the first three resonance frequencies of the arch are generated for various values of initial rise under both tensile and compressive axial loads. This study shows that increasing the tensile or compressive axial loads for different values of initial rise may lead to either increase in the stiffness of the beam or initial decrease in the stiffness, which later increases as the axial load is increased depending on the dominant effect of the initial rise of the arch and the axial load. The obtained universal curves represent useful design tools to predict the tunability of arches under axial loads for various values of initial rises. The use of the universal curves is demonstrated with an experimental case study. Analytical formulation is developed to predict the point of minimum where the trend of the resonance frequency versus axial loads changes qualitatively due to the competing effects of axial loads and initial curvature.

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Figures

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Fig. 1

Schematic diagram for axially loaded arch beam

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Fig. 2

Variation of the critical buckling load with the initial rise

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Fig. 3

(a) Variation of the static deflection around the equilibrium point against the axial load for initial rises from 0.1 to 1 and (b) enlarged view of (a) around the origin

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Fig. 4

(a) Variation of the static deflection around the equilibrium point against the axial load for initial rises from 3 to 10 and (b) enlarged view of (a) around the origin

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Fig. 5

(a) Variation of the first resonance frequency versus axial loads for initial rises from 0.1 to 10 and (b) the enlarged view of (a) around the inflection points

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Fig. 6

A three-dimensional plot of the first resonance frequency against the axial load and initial rise

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Fig. 7

(a) Variation of the third resonance frequency versus axial loads for initial rises from 0.1 to 10 and (b) an enlarged view of (a) around the inflection points

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Fig. 8

(a) Variation of the fifth resonance frequency against axial loads for initial rise from 0.1 to 10 and (b) the zoom view of (a) around the inflection point

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Fig. 10

Comparison of the first natural frequency obtained from the universal curves and experimental data obtained from the electrothermally actuated arch resonator [44]

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Fig. 9

Variation of the critical axial load, at which there is a minimum of the frequency-axial load curve, with the initial rise

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