Nonlocal elastic theory for vibration of fluid-filled double-walled carbon nanotubes

The vibration characteristics of fluid-filled double-walled carbon nanotubes are investigated and vibrational equations are established based on the nonlocal elastic theory and Flügge shell theory in this paper. By considering simple supported boundary conditions, the fundamental frequency of carbon nanotubes is obtained. In the numerical calculation, the effects of wave numbers, geometric and material parameters on vibration frequency are analyzed, while effects of local and nonlocal elastic theories are also discussed. The results showed that the frequency decreased with the increase of the diameter, the length of nanotubes and the value of small scaling parameters.