Nonlinear Vibration of Multi-walled Carbon Nanotubes

Abstract—The nonlinear vibration behavior of a multi-walled carbon nanotube is investigated based on an elastic multi-layer shell model with van der Waals interaction taken into consideration. The multi-walled carbon nanotube is described as an individual elastic shell and the interlayer friction is negligible between the inner and outer tubes in the proposed model. And the Donnell equations of cylindrical shells are employed to describe the nonlinear behavior of the multi-walled carbon nanotubes. The van der Waals interaction between each layer of the nanotubes is simulated based on a new model. Numerical analyses are carried out to simulate several nonlinear vibration processes of different nanotubes. Following results show that the presence of van der Waals interaction forces can strongly influence the buckling and nonlinear vibration of the multi-walled carbon nanotubes. Index Terms—Carbon nanotubes; Nonlinear vibration; continuum shell model; van der Waals interaction. I.