Axial vibration of double-walled carbon nanotubes using double-nanorod model with van der Waals force under Pasternak medium and magnetic effects

The present study investigates the axial vibration of double-walled nanotubes. Using nanorod continuum model with van der Waals effect, vibrational frequencies are studied. Aydogdu (Journal Vibration and Control, Vol. 21, Issue 16, (2015), 3132-3154) proposed a reliable for in nanotube. This provided detailed investigation using effects. But sometimes, wrong equation might lead to erroneous scientific results. incorrect term nanotube is taken care correct inferences. Effectively, appear without decoupling as primary secondary semi-analytical method estimates coupled model. Two different boundary conditions like clamped-clamped clamped-free support, considered this computation. Pasternak medium support magnetic effects influence first second time. constant parameters don't vary length vibration. It means that still more understanding requires modeling force double-nanotube