Comparison for Effect of Nonlocal Parameter on Vibrations of Nanotubes, Based on Exact Solutions of Euler, Timoshenko and Sanders Theories

Vibrational behavior of nanotubes is investigated in different papers based on different theories which our investigation shows that there is big difference in their results. So, in this paper, vibrational behavior of nanotubes is analyzed using Euler, Timoshenko beam theories and Sanders first order shear deformation shell theory. In order to considering effect of scale, nonlocal elasticity theory is combined with these three geometrical theories who are exactly solved for six combinations of classical boundary conditions. Results are compared with references and molecular dynamics results and validity and accuracy of presented methods are approved. It is approved that nonlocal Sanders first order shear deformation theory has the best accuracy and needs the lower scale parameter to predict natural frequencies.