Static and dynamic pull-in instability of multi-walled carbon nanotube probes by He's iteration perturbation method

A continuum model is utilized to extract the nonlinear governing equation for Carbon nanotube (CNT) probes near graphite sheets. The van der Waals (vdW) intermolecular force and electrostatic actuation are included in the equation of motion. Static and dynamic pull-in behavior of the system is investigated in this paper. To this end, a new asymptotic procedure is presented to predict the pull-in instability of electrically actuated CNTs by employing an analytic approach namely He's iteration perturbation method (IPM). The effects of basic non-dimensional parameters such as initial amplitude, intermolecular force, geometrical parameter and actuation voltage on the pull-in instability as well as the fundamental frequency are studied. The obtained results from numerical simulations by employing three mode assumptions verify the strength of the analytical procedure. The qualitative analysis of the system dynamics shows that the equilibrium points of the autonomous system include stable center points and unstable saddle nodes. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits.