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.