Free vibrations of elastically embedded stocky single-walled carbon nanotubes acted upon by a longitudinally varying magnetic field

The mechanical properties of nano-scaled composites reinforced by carbon nanotubes are enhanced by application of appropriate magnetic fields, however, little is known on the free dynamic response of the magnetically affected stocky single-walled carbon nanotubes (SWCNTs) with elastic supports. Using nonlocal Rayleigh, Timoshenko, and higher-order beam theory, the equations of free transverse vibration of elastically embedded SWCNTs subjected to a longitudinally varying magnetic field are obtained. Since finding an analytical solution to the equations of motion is a very difficult task, an efficient meshless method is proposed. The frequencies of the magnetically affected stocky SWCNTs are evaluated for different boundary conditions. The convergence checks of the proposed numerical models are carried out. In a special case, the obtained results are also compared with those of assumed mode method, and a reasonably good agreement is achieved. Subsequently, the roles of the slenderness ratio of the SWCNT, small-scale parameter, strength of the magnetic field, lateral and rotational interactions of the SWCNT with its surrounding medium on the fundamental frequency are addressed in some detail. The capabilities of the proposed models in capturing the frequencies of the magnetically affected nanostructure are also comprehensively investigated.