Nonlocal vibration and pull-in instability analysis of electrostatic carbon-nanotube based NEMS devices

The objective of this paper is to investigate dynamical pull-in behavior of an electrostatic actuated nano-device based on Eringen's nonlocal elasticity theory. The Euler-Bernoulli beam model is used to establish the dynamic equation of motion of the nano-device subjected to both electrostatic and intermolecular forces. The nanobeam is considered with axially immovable ends and the geometrically nonlinearity due to mid-plane stretching is incorporated to the model as well. A new intermolecular attractive force model based on the macroscopic interactions of a circular cross section nanobeam and a flat surface is presented for the carbon nanotube based nano-device. The nonlinear static equation and the linear dynamic equation are treated by the Differential Quadrature Method (DQM) and through a comprehensive survey, the effect of small scale parameter, DC voltage, intermolecular force, residual stress and geometrical nonlinearity on the fundamental natural frequency and pull-in phenomenon are studied. The results are verified with the literature and a good agreement is achieved.