Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory

• A model is derived for viscoelastic SWCNT with surface effect under magnetic field.
• Closed-form dispersion relation between phase velocity and wave number is derived.
• Size-dependent effect on the phase velocity is significant at high wave numbers.
• Phase velocity can increase by decreasing damping or increasing magnetic intensity.
• Damping ratio increases by increasing wave number or decreasing magnetic intensity.

The governing equation of wave motion of viscoelastic SWCNTs (single-walled carbon nanotubes) with surface effect under magnetic field is formulated on the basis of the nonlocal strain gradient theory. Based on the formulated equation of wave motion, the closed-form dispersion relation between the wave frequency (or phase velocity) and the wave number is derived. It is found that the size-dependent effects on the phase velocity may be ignored at low wave numbers, however, is significant at high wave numbers. Phase velocity can increase by decreasing damping or increasing the intensity of magnetic field. The damping ratio considering surface effect is larger than that without considering surface effect. Damping ratio can increase by increasing damping, increasing wave number, or decreasing the intensity of magnetic field.