Modeling Electrostatic Actuator Pull in Behavior With Proper Orthogonal Decomposition

Electrostatic operation has become one of the most common actuation/sensing techniques due to its ease of integration in complex micro-electro-mechanical-systems (MEMS). A critical issue with electrostatic operation is the avoidance of pull in phenomenon. While analytical solutions based on lumped model assumptions are available, finite element method (FEM) has increasingly been used to study pull in phenomenon of intricate devices. Geometrically complex designs require large discretized FEM models to obtain accurate simulations resulting in MEMS designers continually reaching FEM limits due to excessive demands on CPU-time and memory resources. Proper orthogonal decomposition (POD) has been investigated to improve computational efficiency by generating reduced models that capture the pull in characteristics of an electrostatic device. An FEM model of an electrostatically actuated micro resonator beam structure was produced. Employing POD, a basis function was generated that characterized the pull in behavior of the full scale model. The basis function was used to assemble a reduced model. Pull in analysis was performed with the reduced and full FEM models for comparison. It was found that the reduced model achieved similar results as compared to the full model while the computational time was drastically reduced.© 2010 ASME