The thermal effect on nonlinear oscillations of carbon nanotubes with arbitrary boundary conditions

A single-beam model is presented for investigating the nonlinear vibrations of single-walled carbon nanotubes (SWNTs) embedded in an elastic medium. The thermal effect is also incorporated into the formulation. The variational iteration method is used to solve the corresponding nonlinear differential equation. The amplitude–frequency curves for large-amplitude vibrations are graphically illustrated. The influences of thermal effect, some commonly used boundary conditions, changes in material constant of the surrounding elastic medium and variations of geometrical parameters on the vibration characteristics of nanotubes are studied. The results obtained are compared, where possible, with those from the open literature. This comparison clarifies the accuracy as well as the capability of the present method.

Research highlights
► The nonlinear vibration frequency of nanotubes rises rapidly with increasing the amplitude especially when the stiffness of the medium is relatively small.
► At low or room temperature the nonlinear frequencies for the nanotube including the thermal effect are larger than that excluding the thermal effect.
► At high temperatures the nonlinear frequencies decrease with increasing temperature.
► With the increase of the aspect ratio of the nanotubes, the nonlinear vibration frequencies of SWNTs decrease.