Nonlinear Vibrations of a Carbon Nanotube Resonator Under Electrical and van der Waals Forces

In this paper a clamped–clamped single-walled carbon nanotube (SWNT) is modeled using a nonlinear Euler–Bernoulli beam theory. The SWNT is under a nonlinear electrical force created by DC and AC components. Nonlinear van der Waals forces acting between the SWNT and the ground plane, are added to the model, due to the small gap between them. The values of the deflections and the natural frequencies of the SWNT under different values of the DC voltage are studied and compared to the similar works. Adding an AC voltage to the initial DC excitation voltage, an equation is derived for large amplitude vibrations of the nanotube. The multiple-scale perturbation method is used to solve this equation. Finally, the influence of changing different parameters on the behaviour of the SWNT, which can be used for design and optimization of NEMS devices, is also studied according to the obtained equations.