A modified model for dynamic instability of CNT based actuators by considering rippling deformation, tip-charge concentration and Casimir attraction

Abstract

The tip charge concentration and rippling phenomenon can substantially affect the electromechanical performance of actuators fabricated from cantilever carbon nanotube (CNT). However, these important phenomena are often ignored in the theoretical beam models. In this article, the influence of rippling deformation, Casimir attraction and tip concentration charge on the dynamic pull-in characteristics of nanotube actuators is investigated using a modified Euler–Bernoulli beam theory. To express the Casimir attraction of cylinder-plate geometry, two approaches e.g. proximity force approximation (PFA) for small separations and Drichlet asymptotic approximation for large separations are considered. The charge concentration at the CNT tip is included in the governing equation using Dirac delta function. It is demonstrated that the rippling deformation and tip charge concentration can substantially decrease the dynamic pull-in voltage of the nano-actuator. The rippling deformation of CNT increases the pull-in time while the concentrated charge at the CNT end reduces the pull-in time of the nano-system. Results of the present study are beneficial to precise design and fabrication of electromechanical CNT actuators. Comparison between the obtained results and those reported in the literature by experiments and molecular dynamics, verifies the integrity of the present analysis.