Ali Darvishian - School of Mechanical Engineering, Sharif University of Technology
Hamid Moeenfard - School of Mechanical Engineering, Sharif University of Technology
Hassan Zohoor - School of Mechanical Engineering, Sharif University of Technology
Mohammad Taghi Ahmadian - School of Mechanical Engineering, Sharif University of Technology

The current paper models the coupling effect between torsion and bending in micro/nano mirrors under the combined effect of Casimir force and capillary force. First, the energy method, the principal of minimum total potential energy is utilized for finding the equations governing the deflection and rotation of micro/nano mirror. Then the implicit function theorem is utilized for finding the equations governing the pull-in state of the nano/micro mirror. The related results show that neglecting bending effect can lead to considerable overestimation in predicting the pull-in limits of the nano/micromirror under combined Casimir and capillary forces. It is observed that Casimir force reduces the pull-in angle and pull-in deflection of the supporting torsion beams of the mirror. The static behavior of the mirror under capillary and Casimir loading is also studied and the results reveal that the static behavior of the nano/micromirror under capillary and Casimir forces highly depends on the bending of the torsion beams. The results of this paper can be used for a safe and stable design and fabrication of mirrors using the wet etching process, where the gap between themirror and the underneath substrate is sufficiently small and as a results both capillary and Casimir forces have significant role in the stability of the system.

Nano/micromirror, Casimir force, Capillary force, Coupled bending-torsion model, Pull-in