Theoretical study of the effect of Casimir attraction on the pull-in behavior of beam-type NEMS using modified Adomian method

In this paper, modified Adomian decomposition (MAD) is introduced to investigate the effect of the Casimir attraction on pull-in instability of beam-type NEMS theoretically. Two engineering cases including cantilever and double cantilever nano-beam are considered. The proposed MAD method is employed to solve the nonlinear constitutive equation of nano-beams. The basic engineering parameters such as critical deflection and pull-in voltage of nano-beams are computed. It is found that the Casimir forces decrease the pull-in deflection and voltage of nano-beams. On the other hand, the fringing field increases the pull-in deflection while decreases the pull-in voltage of the actuators. As a special case in this work, the instability of freestanding nano-beams is investigated due to the Casimir attraction. The analytical MAD solutions are compared with numerical ones and lumped model, as well as other methods in the literature.