Effect of Membrane Load on the Stability of an Electrostatically Actuated Initially Curved Circular Micro Plate

Abstract

The effects of membrane load on the axisymmetric bistable behavior of circular curved micro plates are studied via an axisymmetric reduced order (RO) model, incorporating radial prestress. The model is based on Kirchhoff’s hypothesis and Föppl-von-Kármán’s kinematics. The model is first validated for a “mechanical” (displacement-independent) load, against an RO model with 20 degrees-of-freedom (DOF), a finite differences (FD) solution, and finally, a finite elements (FE) model, serving as the reference. All solutions implement the “Riks” continuation method to track unstable branches, which can swerve in a complex form due to the presence of higher buckling modes. A convergence study is carried out for the snap-through location and load, as well as for the critical elevation and prestress required for bistability. Based on the validated results of the mechanical analysis, the reliability of the model for predicting the effect of prestress on the plate behavior under nonlinear (displacement-dependent) electrostatic load is then investigated while using FD as the reference. The study furnishes an expended RO model for curved plates, which includes the effect of prestress. The resulting model can further be used to estimate the value of residual membrane load present in electrostatically actuated curved plates, as well as predict the threshold for bistability.