Nonlinear vibrations of multiwalled carbon nanotubes based on coupled displacement field theory using HPM

In this paper, the problem of nonlinear vibrations of multiwalled carbon nanotubes embedded in an elastic medium is investigated. A multiple-beam model based upon the coupled field theory is utilized in which the equations of motion for each layer are coupled with those of its adjacent ones through the van der Waals interlayer interactions. The system of coupled nonlinear differential equations is analytically solved by the homotopy perturbation method. The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled and triple-walled nanotubes are graphically illustrated. The effects of material constant of the surrounding elastic medium and the geometric parameters on the vibration characteristics are investigated. The amplitude-frequency curves obtained have been compared with those of previously reported counterparts in the published literature. This comparison illustrates that the solutions obtained are of very high accuracy and clarifies the capability and the simplicity of the present method.