Size-dependent pull-in instability analysis of electrically actuated packaged FG micro-cantilevers under the effect of mechanical shock

This paper focuses on analyzing the unstable behavior of an electrically actuated functionally graded micro-cantilever under the effect of mechanical shock based on the modified couple stress theory. Since the micro-devices are usually mounted on some packages, the effect of packaging on the behavior of the system is also investigated. To this end, Hamilton’s principle is employed to derive the governing equation of motion base on the Euler–Bernoulli beam theory. Afterward, Galerkin’s method is used to convert the governing partial differential equation of motion to a single initial value problem. The accuracy of the presented results is also validated by comparison with available findings in the literature. Furthermore, a detailed parametric study is conducted to investigate the effect of mechanical shock on the behavior of the micro-cantilever. MEMS devices are usually actuated with electrostatic force, so the combined effect of electrostatic and mechanical shock is presented afterward. The packaging effect is also modeled with a micro-beam mounted on a single-degree-of-freedom mass and spring system. It is shown that not considering the MEMS packaging will lead to false results.