Vibration of multi-walled carbon nanotubes by generalized shear deformation theory

In this study, free vibration of simply supported multi-walled carbon nanotubes (CNTs) was investigated by using the generalized shear deformation-beam theory (GSDBT). Parabolic shear deformation theory (PSDT) is used in the specific solutions. Unlike Timoshenko beam theory present theory satisfies zero traction boundary conditions on the upper and lower surface of the structures so there is no need to use a shear correction factor. Free vibration frequencies and amplitude ratios were obtained and results are compared with previous studies. Results showed that significant difference exist between PSDT and Euler beam theory. Present results are slightly higher than the results of Timoshenko beam theory. Shear deformation effects are important especially for higher modes. It is obtained that van der Waals (vdW) forces should be considered for small inner radius.