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

Abstract

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