Simple and accurate analytical solution to the post-buckling response of an electrostatically actuated MEMS curled cantilever

In this work, we propose to investigate the micro-electromechanical post-buckling response of an electrostatically-actuated curled cantilever microbeam. The analytical/numerical model is based on a nonlinear differential governing equation, derived via assuming a continuous Euler–Bernoulli beam model, combined with a multi-modes Galerkin decomposition of the beam deflection. The pull-in voltages which govern the stability of the micro-curled beam actuator are also obtained analytically. These approximate solutions show excellent agreements compared to solutions obtained by other computationally expensive numerical methods as well some previously reported experimental data, for a wide range of the microbeam length. The derived expressions of these analytical approximate solutions are easy to implement, quick to solve, and could be conveniently used by MEMS designers for quick estimations of the effects of the various micro-actuator parameters on its structural stability.