Modeling the Effect of Van Der Waals Attraction on the Instability of Electrostatic Cantilever and Doubly-supported Nano-beams Using Modified Adomian Method

A nano-scale continuum model is applied to investigating the effect of van der Waals (vdW) attraction on pull-in instability of nano-beams in the presence of electrostatic forces. Two cases including the cantilever and doubly-supported beams are considered. The modified Adomian decomposition (MAD) method is employed to solve the nonlinear constitutive equation of nano-beams in the presence of vdW and electrostatic forces for the first time. The results show that the effect of vdW attraction on the instability of the doubly-supported nano-beam is weak when compared to that of the cantilever due to the higher elastic stiffness of the former. Basic design parameters such as the critical deflection and pull-in voltage of the nano-beam are computed. The minimum initial gap and the detachment length of an actuator that does not stick to the substrate due to intermolecular attractions are determined. As a special case, the instability of freestanding nano-electromechanical systems (NEMS) due to vdW attraction is investigated. The MAD solutions are compared with the numerical ones and a proposed lumped model, as well as models available from the literature.