Refined shell models for the vibration analysis of multiwalled carbon nanotubes

The free vibration response of double-walled carbon nanotubes is studied in this article. A continuum approach is used and refined shell models are obtained through the application of Carrera's Uni- fied Formulation (CUF). In order to apply the continuum models, the multi-walled carbon nanotube is assumed to be a multilayer cylindrical shell with an equivalent thickness and Young's modulus. Equivalent single-layer and layer-wise approaches in CUF are modified to consider the nested tubes of a multi-walled carbon nanotube as independent and separately vibrating. The van der Waals interaction between two adjacent tubes is estimated by using the Lennard-Jones model. The proposed results emphasize the differences that exist among available continuum models and present shell approaches. In particular, the attention is devoted to van der Waals interaction and a comparison has been made between models that take into account the van der Waals forces and models that neglect them.