Effect of the Casimir attraction on the torsion/bending coupled instability of electrostatic nano-actuators

In this paper, the effect of the Casimir attraction on the torsion/bending coupled pull-in instability of an electrostatic nano-actuator has been investigated for the first time. The governing equation of the actuator is derived and the instability parameters of the nano-actuator have been computed as a function of the geometrical characteristics and the bending/torsion stiffness ratio of the nano-actuator. The results reveal that the Casimir attraction could highly affect the coupled pull-in performance of the actuator. It is found that the Casimir force can reduce the instability voltage of nano-actuators. This deteriorating effect is more clearly highlighted in the torsional pull-in mode compared to the bending pull-in mode. Furthermore, it is found that the influence of the Casimir force on pull-in angle and deflection of the torsional actuator depends on the torsion/bending coupling ratio. For small-gap torsional actuators, the pull-in parameters have been strongly affected by the Casimir force, and neglecting Casimir attraction may lead to considerable error during simulations of the pull-in instability. The results of the present model are in better agreement with the experimental data compared to previous models.