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Stochastic modeling of coupled electromechanical interaction for uncertainty quantification in electrostatically actuated MEMS
 

Summary: Stochastic modeling of coupled electromechanical interaction
for uncertainty quantification in electrostatically actuated MEMS
Nitin Agarwal, N.R. Aluru *
Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois
at Urbana-Champaign, 405 N. Mathews Avenue, Urbana, IL 61801, United States
Received 20 August 2007; received in revised form 11 December 2007; accepted 16 January 2008
Available online 26 January 2008
Abstract
This work proposes a stochastic framework based on generalized polynomial chaos (GPC), to handle uncertain coupled electrome-
chanical interaction, arising from variations in material properties and geometrical parameters such as gap between the microstructures,
applicable to the static analysis of electrostatic MEMS. The proposed framework comprises of two components a stochastic mechan-
ical analysis, which quantifies the uncertainty associated with the deformation of MEM structures due to the variations in material prop-
erties and/or applied traction, and a stochastic electrostatic analysis to quantify the uncertainty in the electrostatic pressure due to
variations in geometrical parameters or uncertain deformation of the conductors. The stochastic analysis is based on a stochastic
Lagrangian approach, where, in addition to uncertain input parameters and unknown field variables, the random deformed configura-
tion is expanded in terms of GPC basis functions. The spectral modes for the unknown field variables are finally obtained using Galerkin
projection in the space spanned by GPC basis functions. The stochastic mechanical and electrostatic analyses are performed in a self-
consistent manner to obtain the random deformation of the MEM structures. Various numerical examples are presented to study the
effect of uncertain parameters on performance of various MEMS devices. The results obtained using the proposed method are verified
using rigorous Monte Carlo simulations. It has been shown that the proposed method accurately predicts the statistics and probability

  

Source: Aluru, Narayana R. - Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign

 

Collections: Engineering; Materials Science