Size-Dependent Dynamic Behavior and Instability Analysis of Nano-Scale Rotational Varactor in the Presence of Casimir Attraction

When the size of structures approaches to the sub-micron scale, physical responses of such systems become size-dependent, hence, classic theories may not be able to predict the behavior of the miniature structures. In the present article, the modified couple stress theory (MCST) is employed to account for the effect of the size-dependency on the dynamic instability of torsional nano-electromechanical systems (NEMS) varactor. By incorporating the Coulomb, Casimir and damping forces, the dimensionless governing equations are derived. The influences of Casimir force, applied voltage and length scale parameter on the dynamic behavior and stability of fixed points are investigated by plotting the phase portrait and bifurcation diagrams. It is found that the Casimir force reduces the instability threshold of the systems and the small-scale parameter enhances the torsional stability. The pull-in instability phenomenon shows the saddle-node bifurcation for torsional nano-varactor.