Nonlinear pull-in instability and free vibration of micro/nanoscale plates with surface energy – A modified couple stress theory model

• A reduced-order model for electrostatically actuated nanoplates is developed.
• The model including material length scale, surface energy and geometric nonlinearity.
• Pull-in parameters are enhanced by the material length scale and surface energy.
• Effect of Casimir force on pull-in parameters is remarkable for small plate gap.

Effects of surface energy on the pull-in instability and free vibration of electrostatically actuated micro/nanoscale plates are analyzed based on the modified couple stress theory. A reduced-order model is derived to consider the geometrically nonlinear strain, surface energy, the Casimir force and the material length scale simultaneously. Results show that the pull-in voltage and fundamental frequency of the plate are considerably enhanced by the material length scale, surface energy and geometrically nonlinear deformation. However, these quantities are weakened with the inclusion of Casimir force. The effects of surface energy and the material length scale become more significant if the thickness decreases. In addition, the effects of surface energy and geometrically nonlinear strain on the pull-in voltage are the largest for a square plate.