Using Modified Couple Stress Theory for Modeling the Size-Dependent Pull-In Instability of Torsional Nano-Mirror under Casimir Force

It is well-established that mechanical response of nanostructures is size-dependent. In this article, the size-dependent pull-in instability of rotational nano-mirror is investigated using modified couple stress theory. The governing equation of the mirror is derived taking the effect of electrostatic Coulomb and Casimir forces into account. Effect of finite conductivity of material is included in the Casimir formulation. Variation of the rotation angle of the mirror as a function of the applied voltage is obtained and the instability parameters i.e., pull-in voltage and pull-in angle of the system are determined. The effect of Casimir forces on the size-dependent pull-in instability of the system is discussed. Furthermore, the minimum gap between the mirror and the ground to prevent stiction (due to Casimir force) is determined as a function of material length scale parameter. It is found that the proposed model is able to predict the experimental results more accurately than the previous classical models and reduces the gap between previous theories and experiments.