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Characterization of the mechanical behavior of an electrically actuated microbeam

Eihab M Abdel-Rahman, Mohamed I Younis and Ali H Nayfeh

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We present a nonlinear model of electrically actuated microbeams accounting for the electrostatic forcing of the air gap capacitor, the restoring force of the microbeam and the axial load applied to the microbeam. The boundary-value problem describing the static deflection of the microbeam under the electrostatic force due to a dc polarization voltage is solved numerically. The eigenvalue problem describing the vibration of the microbeam around its statically deflected position is solved numerically for the natural frequencies and mode shapes. Comparison of results generated by our model to the experimental results shows excellent agreement, thus verifying the model. Our results show that failure to account for mid-plane stretching in the microbeam restoring force leads to an underestimation of the stability limits. It also shows that the ratio of the width of the air gap to the microbeam thickness can be tuned to extend the domain of the linear relationship between the dc polarization voltage and the fundamental natural frequency. This fact and the ability of the nonlinear model to accurately predict the natural frequencies for any dc polarization voltage allow designers to use a wider range of dc polarization voltages in resonators.


PACS

07.10.Cm Micromechanical devices and systems

46.70.De Beams, plates and shells

46.40.Ff Resonance, damping and dynamic stability

02.60.Lj Ordinary and partial differential equations; boundary value problems

Subjects

Computational physics

Instrumentation and measurement

Condensed matter: structural, mechanical & thermal

Dates

Issue 6 (November 2002)

Received 10 January 2002, in final form 7 August 2002

Published 5 September 2002



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