Modeling the effects of size dependence and dispersion forces on the pull-in instability ofelectrostatic cantilever NEMS using modified couple stress theory

Abstract

An electromechanical beam-type nano-actuator is one the most important smartnanostructures. In this paper, modified couple stress theory is used to model the size effecton the static pull-in instability of electrostatic nanocantilevers in the presence of dispersion(Casimir/van der Waals) forces. The monotonically iterative method (MIM) and homotopyperturbation method (HPM) are employed to solve the nonlinear constitutiveequation of the nanostructure as well as numerical methods. Furthermore, a lumpedparameter model is developed to explain the size-dependent pull-in performance ofthe nano-actuator. The basic engineering design parameters such as critical tipdeflection and pull-in voltage of the nanostructure are computed. It is found thatdispersion forces decrease the pull-in voltage and deflection of the nano-actuator atsub-micrometer scales. On the other hand, the size effect can increase the pull-inparameters of the nano-actuators. The results indicate that the proposed analyticalsolutions are reliable for simulating nanostructures at sub-micrometer ranges.