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On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators

Fadi M Alsaleem, Mohammad I Younis and Hassen M Ouakad

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We present modeling, analysis and experimental investigation for nonlinear resonances and the dynamic pull-in instability in electrostatically actuated resonators. These phenomena are induced by exciting a microstructure with nonlinear forcing composed of a dc parallel-plate electrostatic load superimposed on an ac harmonic load. Nonlinear phenomena are investigated experimentally and theoretically including primary resonance, superharmonic and subharmonic resonances, dynamic pull-in and the escape-from-potential-well phenomenon. As a case study, a capacitive sensor made up of two cantilever beams with a proof mass attached to their tips is studied. A nonlinear spring–mass–damper model is utilized accounting for squeeze-film damping and the parallel-plate electrostatic force. Long-time integration and a global dynamic analysis are conducted using a finite-difference method combined with the Floquet theory to capture periodic orbits and analyze their stability. The domains of attraction (basins of attraction) for data points on the frequency–response curve are calculated numerically. Dover cliff integrity curves are calculated and the erosion of the safe basin of attraction is investigated as the frequency of excitation is swept passing primary resonance and dynamic pull-in. Conclusions are presented regarding the safety and integrity of MEMS resonators based on the simulated basin of attraction and the observed experimental data.


PACS

85.85.+j Micro- and nano-electromechanical systems (MEMS/NEMS) and devices

07.07.Df Sensors (chemical, optical, electrical, movement, gas, etc.); remote sensing

Subjects

Electronics and devices

Instrumentation and measurement

Nanoscale science and low-D systems

Dates

Issue 4 (April 2009)

Received 1 August 2008, in final form 11 February 2009

Published 17 March 2009



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