Rigorous van der Waals effect on vibration characteristics of multi-walled carbon nanotubes under a transverse magnetic field

An analytical method is presented to investigate rigorous van der Waals interaction effect on vibration characteristics of multi-walled carbon nanotubes embedded in matrix under a transverse magnetic field. Each of the concentric tubes of multiwall carbon nanotubes is considered as an individual elastic shell and coupled with any two walls through a rigorous van der Waals interaction being dependent on the change of interlayer spacing and the radii of tubes. Results show that the rigorous van der Waals interaction effect makes the lowest magneto-vibration frequency of multi-walled carbon nanotubes decrease and the highest magneto-vibration frequency increase. The effect of rigorous van der Waals interaction on magneto-elastic vibrations of multi-walled carbon nanotubes is dependent on the transverse magnetic strength and the matrix constrained stiffness.