Analysis of nonlinear vibration for embedded carbon nanotubes

Based on the continuum mechanics and a multiple-elastic beam model, the nonlinear free vibration of embedded multi-wall carbon nanotubes considering intertube radial displacement and the related internal degrees of freedom is investigated. By using the incremental harmonic balanced method, the iterative relationship of nonlinear amplitude and frequency for the single-wall nanotube and double-wall nanotube are expressed. In the numerical calculation, the amplitude frequency response curves of the nonlinear free vibration for the single-wall and double-wall nanotubes are obtained. The effects of the surrounding elastic medium, van der Waals forces and aspect ratio of the multi-wall nanotubes on the amplitude frequency response characteristics are discussed.