On the influence of the shear deformation and boundary conditions on the transverse vibration of multi-walled carbon nanotubes

The vibrational properties of multi-walled carbon nanotubes (MWCNTs) are studied, especially the influence of the shear deformation and the boundary conditions on the non-coaxial frequencies. A high order continuum beam model is proposed, which can be applied to study the transverse vibrations of MWCNTs, including those that could have initial deformations due to defects or external actions. Using the model it was found that the non-coaxial intertube frequencies are independent of the shear deformation and the boundary conditions. This result is important considering that the concentric structure of MWCNTs is a crucial geometrical characteristic and a non-coaxial vibration would affect their electronic and optical properties.