Nonlocal Timoshenko beam model for the large-amplitude vibrations of embedded multiwalled carbon nanotubes including thermal effects

A nonlocal Timoshenko beam model is developed to study the nonlinear vibrations of embedded multiwalled carbon nanotubes (MWCNTs) in thermal environments. The Timoshenko beam model, unlike its Bernoulli–Euler beam counterpart, takes the effects of transverse shear deformation and rotary inertia into consideration. These effects become more significant for short-length nanotubes that are normally encountered in applications such as nanoprobes. The nested nanotubes are coupled via the van der Waals (vdW) force that considers interactions between adjacent and non-adjacent nested nanotubes. The set of coupled nonlinear equations are then analytically solved using the harmonic balance approach. The effects of small-scale parameter, nanotube geometries, temperature change and the elastic medium are investigated.

Graphical AbstractA nonlocal Timoshenko beam model is developed to analytically study the nonlinear vibrations of embedded multiwalled carbon nanotubes (MWCNTs) in thermal environments.Figure optionsDownload as PowerPoint slideResearch highlights
► The harmonic balance method is adopted to study the nonlinear vibrations of MWCNTs.
► The influence of nonlocality on the nonlinear vibrations of MWCNTs is examined.
► In the nonlinear regime, the vdW interaction between all layers of MWCNTs must be included.
► At high temperatures, the nonlinear frequency ratio is higher than that of the zero temperature.
► At low temperature, however, this frequency ratio is lower than that of the zero temperature.