A modified model for circular scanner-type nano-mirrors with size-dependency, squeeze film damping and Casimir effects by considering finite conductivity

For the case of micro/nano-scale structures, it is well-known that the physico-mechanical behavior of such devices is size-dependent. However, the classical continuum theory cannot correctly predict the size-dependency. In this paper, the modified couple stress theory is employed to examine the instability characteristics of scanner-type nano-mirrors with circular geometry. The governing equation of the scanner is derived incorporating the effects of electrostatic Coulomb and corrected Casimir forces with the consideration of the finite conductivity of interacting surfaces. In addition, to investigate the influence of air damping, a modified nonlinear expression for the squeeze film model is proposed. The influences of vacuum fluctuation, applied voltage, nonlinear damping and length scale parameter on the dynamic instability of equilibrium points are studied by plotting the phase portrait and bifurcation diagrams. It is concluded from the obtained results that the Casimir attraction reduces the instability threshold of the nano-systems. The small-scale parameter and the nonlinear squeeze film damping enhance the torsional stability. In the presence of the applied voltage, the phase portrait shows the saddle-node bifurcation while for free-standing scanner a subcritical pitchfork bifurcation is observed.