Dynamic analysis of a digital micromirror device

G. Chaabane, E. M. Abdel-Rahman, A. H. Nayfeh, S. Choura, Sami El-Borgi, H. Jammoussi

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

Abstract

We developed a distributed-parameter model (partial differential equations and associated boundary conditions) that describe the coupled torsion and bending motions of the Digital Micromirror Device (DMD) using the extended Hamilton principle. The work done by the electrostatic field is expressed in the form of a potential energy. It is found that coupling between the torsion and bending motions appears in the boundary conditions. The nonlinearity is mainly due to the application of the electrostatic forces and moments. Nonlinear terms appear only in the boundary conditions. The developed model provides a basis for a thorough study of the static and dynamic behaviors of the electromechanical device. The static response of the DMD for different DC loads shows the occurrence of pull-in (snap-down) instability at critical voltage values corresponding to the collapse of the yoke to mechanical stops. Estimates of the voltage, angle, and deflection at pull-in are given. The dynamic behavior of the DMD is analyzed by plotting the natural frequencies versus the applied DC voltage. We conducted a study of the sensitivity of the static and dynamic behaviors of the micromirror to variations in the geometric parameters of the DMD. It is found that the thickness and width of the hinges are the key parameters influencing the occurrence of static pull-in and the values of the voltage, angle, and deflection at pull-in.

Original languageEnglish
Title of host publicationProceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Applied Mechanics Division
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Print)0791837904, 9780791837900
DOIs
Publication statusPublished - 2006
Externally publishedYes
Event2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Chicago, IL
Duration: 5 Nov 200610 Nov 2006

Other

Other2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006
CityChicago, IL
Period5/11/0610/11/06

    Fingerprint

ASJC Scopus subject areas

  • Mechanical Engineering

Cite this

Chaabane, G., Abdel-Rahman, E. M., Nayfeh, A. H., Choura, S., El-Borgi, S., & Jammoussi, H. (2006). Dynamic analysis of a digital micromirror device. In Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Applied Mechanics Division American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/IMECE2006-14010