Nonlinear vibration and stability analysis of a double-walled carbon nanotube under electrostatic actuation

In this paper, forced vibrations of a double-walled clamped–clamped carbon nanotube (DWNT) are studied. Two Euler–Bernoulli beams are used to model the inner and outer layers of the DWNT. An electrostatic actuation, which is comprised of DC and AC voltages is applied between the nanotubes and the electrode. In the system model, the nonlinear form of the interlayer van der Waals (vdW) force, and also, the mid-plane stretching are considered. The obtained equations are solved through Galerkin and multiple scales methods for primary and secondary resonances. The frequency response of the system is obtained as a function of some of the system parameters. A stability analysis of the response is conducted and bifurcation points are determined. The results demonstrate that the DWNT shows different behavior by changing the value of DC voltage. It is also observed that both layers of the DWNT vibrate with the same frequency under the primary and secondary resonance conditions.