Static pull-in instability analysis of beam type NEMS under molecular force using strain gradient theory

In this paper، stress gradient theory is used to model the static pull-in instability and size effect of electrostatic nanocantilevers in the presence of electrostatic and dispersion (Casimir/van der Waals) forces. The Differential transformation method (DTM) is employed to solve the nonlinear constitutive equation of the nanostructure as well as numerical methods. The basic engineering design parameters such as critical tip deflection and pull-in voltage of the nanostructure are computed. It is found that in the presence of dispersion forces، both pull-in voltage and deflection of the nanobeam increase with increasing the size effect. Compared to the pull-in voltage، the pullin deflection of the beam is less sensitive to the size effect at sub-micrometer scales. On the other hand، the size effect can increase the pull-in parameters of the nano-actuators only in sub-micrometer scales. The results indicate that the proposed analytical solutions are reliable for simulating nanostructures at sub-micrometer ranges.