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

This work proposes a stochastic framework based on generalized polynomial chaos (GPC), to handle uncertain coupled electromechanical 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 mechanical analysis, which quantifies the uncertainty associated with the deformation of MEM structures due to the variations in material properties 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 configuration 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 density functions of various relevant parameters.