Modeling the Influence of Van der Waals Force on the Size-dependent Pull-in Instability of Torsional Nano actuator Using Torsion/bending Model

In this study, the effect of nano scales, van der Waals intermolecular force and steretching effect on the torsion-bending coupled pull-in instability parameters of torsional nano-mirror by using higher order strain gradient theory have been considered. In this model, the modified strain gradient theory, governing equations of system are derived then instability variables such as pull-in angle, pull-in displacement and pull-in voltage versus geometric and material characteristics are investigated and obtained results compared with experimental results. Results show that van der Waals force have much effects on nano-mirror performance. Furthermore, it is found that influence of van der Waals force on the changes of pull-in variables of nano-mirror depends on bending-torsion stiffness ratio and neglecting van der Waals attraction may lead to considerable error during simulations of pull-in instability. Therefore steretching effect similar to van der Waals force could highly affects pull-in parameters for small-gap torsional mirrors that increased pull-in parameters of system. Interestingly, the present model is able to predict experimental results well and more accurately than previous classic models and reduce the gap between experimental results with previous theories.