Size-dependent pull-in instability of torsional nano-actuator

It is well established that the mechanical behavior of ultra-small elements is size-dependent. In this paper, strain gradient continuum theory is applied for modeling the size-dependent pull-in instability of torsional nano-actuator. An actuator with a general hexagonal shape main plate is considered. The governing equation of the actuator is derived taking the effect of electrostatic and Casimir forces into account. Variation of the tilt angle as a function of the applied voltage is calculated. Moreover, the pull-in voltage and pull-in angle of the actuator are determined. Results show that when the thickness of the torsional beam is comparable with the intrinsic material length scales, size effect can substantially increase the instability voltage and angle of the rotational actuator. Moreover, the effect of the Casimir force on the size-dependent pull-in instability of the torsional actuator is discussed. Interestingly, the proposed model is able to predict the experimental results more accurately than the previous classic models and reduce the gap between previous theories and experimental measurements.