Background: In the upcoming era carbon nanotubes have proved to be the most promising
material in the field of science and technology. In the analysis of carbon nanotube, nonlocal elasticity is
found to be highly effective as it regards the small scale effects in the analysis. The small scale effect is
found to be considered via nonlocal elasticity in both axial and radial direction.
Objective: In the present article, radial nonlocal effect on the vibration of carbon nanotubes supported in
Winkler type elastic foundation is studied.
Method: In the analysis, Timoshenko beam theory is employed to derive the governing differential
equations. Finite element model is developed.
Results: It is observed radial nonlocal effect has a dominating effect over Winkler modulus parameter
and at higher diameter, the effect of Winkler modulus disappears.
Conclusion: The observation indicates that radial scale effect has significant influence in the vibration
analysis of carbon nanotubes supported on Winkler foundation.