Size dependent pull-in instability analysis of torsional nano/micromirrors in the presence of molecular force using 2D model

In this study, using the higher order modified strain gradient theory, the size-dependent coupled bending/torsion model is developed for the torsional nano-mirror. In this model, the effect of the Casimir force and the mid-plane stretch in beams on the torsion/bending coupled pull-in instability of a torsional nano-mirror is investigated. First, the governing equations are developed by using modified strain gradient theory and by considering the Casimir force and stretching effects and the problems pertaining to the torsional formulation of modified strain gradient theory are solved. Afterwards, the curves of the parameters of instability as a function of geometric specifications, the ratio of bending/torsion coupling, and size effect are drawn. The results demonstrate that the pull-in parameters are affected by the Casimir force and the bending/torsion coupling ratio coefficient and to dispense with these factors results in considerable errors in system simulation. Moreover, the size effect and stretching effect have a strong effect on pull-in parameters. Finally, it is noteworthy that the present model is capable of predicting the experimental result with great precision in comparison to the classical models and is able to shorten the distance between the past theories and the experimental results.