The influence of dispersion forces on the dynamic pull-in behavior of vibrating nano-cantilever based NEMS including fringing field effect

•The influence of dispersion forces on the dynamic pull-in behavior of nano-beams is investigated.•The impact of amplitude of vibration on pull-in instability, pull-in voltage and fundamental frequency of nano-actuators is studied.•The second-order frequency–amplitude relationship is introduced by employing PEM.•The phase portraits of the nano-beam actuator exhibit periodic and homoclinic orbits.

Dynamic pull-in instability of vibrating nano-actuators in the presence of actuation voltage is studied in this paper through introducing the closed form expression for the fundamental frequency of beam-type nano-structure. The fringing field effect and dispersion forces (Casimir and van der Waals attractions) are taken into account in the dynamic governing equation of motion. The influences of initial amplitude of vibration, applied voltage and intermolecular forces on the dynamic pull-in behavior and fundamental frequency are investigated by a modern asymptotic approach namely Parameter Expansion Method (PEM). It is demonstrated that two terms in series expansions are sufficient to produce an acceptable solution of the actuated nano-structure. The obtained results from numerical methods by considering three mode assumptions verify the strength of the analytical procedure. The qualitative analysis of system dynamic shows that the equilibrium points of the autonomous system include stable center points and unstable saddle nodes. The phase portraits of the nano-beam actuator exhibit periodic and homoclinic orbits.