USE OF STRAIN GRADIENT THEORY FOR MODELING THE SIZE-DEPENDENT PULL-IN OF ROTATIONAL NANO-MIRROR IN THE PRESENCE OF MOLECULAR FORCE

Abstract

Experiments reveal that mechanical behavior of nanostructures is size-dependent. Herein, the size dependent pull-in instability of torsional nano-mirror is investigated using strain gradient nonclassic continuum theory. The governing equation of the mirror is derived taking the effect of electrostatic Coulomb and molecular van der Waals (vdW) forces into account. 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 are determined. Nano-mirrors with square and circular cross-sectional beams are investigated as case studies. It is found that when the thickness of the torsional nano-beam is comparable with the intrinsic material length scales, size effect can substantially increase the instability parameters of the rotational mirror. Moreover, the effect of vdW forces on the size-dependent pull-in instability of the system is discussed. The proposed model is able to predict the experimental results more accurately than the previous classic models and reduce the gap between experiment and previous theories.