Experimental and theoretical investigation of the nonlinear dynamics of an electrostatically-actuated device

Fadi M. Alsaleem, Mohammad I. Younis, Hassen M. Ouakad

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)


We present modeling, analysis, and experimental investigation for dynamic instabilities and bifurcations in electrostatically actuated resonators. These instabilities are induced by exciting a microstructure with a nonlinear forcing composed of a DC parallel-plate electrostatic load superimposed to an AC harmonic load. Because of the dominant effect of the electrostatic nonlinearity, several resonances and nonlinear phenomena are induced. Examples of these are the excitation of secondary-resonances, superharmonic and subharmonic, at half and twice the natural frequency of the microstructure. Also, local bifurcations, such as saddle-node and pitchfork, and global bifurcations, such as the escape phenomenon and the homoclinic tangling may occur. These lead to undesirable jumps, hysteresis, and dynamic pull-in instabilities in MEMS devices and structures. The present work represents an attempt to explore these topics in more depth. The first part of this paper is focused on analyzing and studying the nonlinear dynamics of a capacitive device both theoretically and experimentally with a focus on the case of primary-resonance excitation (near the fundamental natural frequency of the structure). The device is made up of two cantilever beams with a proof mass attached to their tips. A nonlinear spring-mass- damper model is utilized, which accounts for squeeze-film damping. Long-time integration for the equation of motion is used to compare with the obtained experimental data. Then, global dynamic analysis is conducted using a finite difference method (primary resonance) and shooting method (subharmonic resonance) combined with the Floquet theory to capture periodic orbits and analyze their stability. The domains of attraction (basins of attraction) for selected data are calculated numerically. Experimental data revealing primary and sub-harmonic resonances, dynamic pull-in, and the escape-from-a-potential- well phenomenon are shown and compared with the theoretical results.

Original languageEnglish
Title of host publication2008 Proceedings of ASME International Mechanical Engineering Congress and Exposition, IMECE 2008
Number of pages10
EditionPART A
Publication statusPublished - Sep 21 2009
Externally publishedYes
Event2008 ASME International Mechanical Engineering Congress and Exposition, IMECE 2008 - Boston, MA, United States
Duration: Oct 31 2008Nov 6 2008

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings
NumberPART A


Conference2008 ASME International Mechanical Engineering Congress and Exposition, IMECE 2008
CountryUnited States
CityBoston, MA

ASJC Scopus subject areas

  • Mechanical Engineering

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