Analytical modeling of dynamic pull-in instability behavior of torsional nano/micromirrors under the effect of Casimir force

In this study, the dynamic stability of torsional electrostatic micro/nano-electromechanical systems (MEMS/NEMS) using single degree of freedom model under Casimir force and size effect is investigated. First, the equation of motion of system is developed. Afterwards, dimensionless equation of motion by using normalized parameters is presented and by considering state space method, dynamic equations are solved and intended results are achieved. Afterwards, pull-in angle and pull-in voltage of system which include the parameters affecting its performance, are investigated and its dependence on Casimir force and size effect are shown. Results show that equilibrium points include center points, stable focus points and unstable saddle points. The phase portraits related to these points exhibit periodic orbits, heteroclinic orbits and homoclinic orbits which with regard to considered particular circumstances for system are illustrated. Furthermore, in present study by using modified couple stress model, the influence of size effect on amplitude and frequency of system is considered. Obtained results show that proposed model is in better agreement with experimental data and is able to shorten the distance between the classic theory and the experimental results.