Transverse vibrations of single-walled carbon nanotubes with initial stress under magnetic field

This article presents an analytical study, by considering the initial stress presence, for the transverse vibrations of single-walled carbon nanotubes under longitudinal magnetic field. The behavior of single-walled carbon nanotube is modelled as a Timoshenko beam. The explicit solutions are derived for both a combined stress/strain and a combined strain/inertia gradient elasticity theories. A numerical application is carried out for a simply supported single walled carbon nanotube. The numerical results showing the effects of initial stress and longitudinal magnetic field are presented in detail, for the different length scale parameters. This analysis reveals new significant findings for the critical buckling stress and the different capabilities of scale parameters under the magnetic field. This work carried out for the effect of longitudinal magnetic field on the wave propagation in the carbon nanotubes containing the initial stress may be useful particularly in the design and applications of nano electro mechanical systems.