Carbon nano-tube (CNT) is applied to fabricate nano-probes, nano-switches, nano-sensors and nano- actuators. In this paper, a continuum model is employed to obtain the nonlinear constitutive equation and pull-in instability of CNT-based probe/actuators, which includes the effect of electrostatic interaction and intermolecular van der Waals (vdW) forces. The modified Adomian decomposition (MAD) method is applied to solve the nonlinear governing equation of the CNT-based actuator. Furthermore a simple and useful lumped parameter model was developed to investigate trends for various pull-in parameters. The influence of the vdW force and the geometrical dimensionless parameter on the pull-in deflection and voltage of the system is investigated. The obtained results are compared with those available in the literature as well as numerical solutions. The results demonstrate that our developed continuum based model is in good agreement with experimental results.

It is well recognized that size dependency of materials characteristics, i.e. size-effect, often plays a significant role in the performance of nano-structures. Herein, strain gradient continuum theory is employed to investigate the size dependent pull-in instability of beam-type nano-electromechanical systems (NEMS). Two most common types of NEMS i.e. nano-bridge and nano-cantilever are considered. Effects of electrostatic field and dispersion forces i.e. Casimir and van der Waals (vdW) attractions have been considered in the nonlinear governing equations of the systems. Two different solution methods including numerical and Rayleigh-Ritz have been employed to solve the constitutive differential equations of the system. Effect of dispersion forces, the size dependency and the importance of coupling between them on the instability performance are discussed.