Effect of membrane load on the stability of an electrostatically actuated initially curved circula micro plate

作者：L. Medina · 发表于：Journal of applied mechanics · 年份：2022 · DOI：10.1115/1.4056059

The effects of membrane load on the axisymmetric bistable behaviour of circular curved micro plates is studied via axisymmetric reduced order (RO) models, incorporating radial prestress. One model is based on the Kirchhoff hypothesis and Föppl-von-Kármán's kinematics, while the second is based on Berger's approximated plate theory. The models are first validated for a “mechanical” (displacement-independent) load, against an RO model with twenty degrees of freedom (DOF), a finite differences (FD) solution and a finite elements (FE) model, serving as the reference. All solutions implement the “Riks” method to track unstable branches, which can swerve in a complex form due to 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 validated results of the mechanical analysis, the reliability of the models for predicting the effect of prestress on the plate behaviour under nonlinear (displacement-dependent) electrostatic load is then investigated, while using FD as the reference. The study furnishes an expended RO model, which includes the effect of prestress on curved plates. The resulting model can further be used to estimate the value of residual present in electrostatically actuated curved plates, as well as predict the threshold for bistability