A continuum shell model including van derWaals interaction for free vibrations of double-walled carbon nanotubes

This paper proposes the free vibration analysis of Double-Walled Carbon Nano Tubes (DWCNTs). A continuum elastic three-dimensional shell model is used for natural frequency investigation of simply supported DWCNTs. The 3D shell method is compared with beam analyses to show the applicability limits of 1D beam models. The effect of van der Waals interaction between the two cylinders is shown for different Carbon Nano Tube (CNT) lengths and vibration modes. Results give the van der Waals interaction effect in terms of frequency values. In order to apply the 3D shell continuum model, DWCNTs are defined as two concentric isotropic cylinders (with an equivalent thickness and Young modulus) which can be linked by means of the interlaminar continuity conditions or by means of an infinitesimal fictitious layer which represents the van der Waals interaction.