Applicability and Limitations of Ru’s Formulation for Vibration Modelling of Double-Walled Carbon Nanotubes

In this paper, a comparison is conducted between two different formulations of the van der Waals interaction coefficient layers, as applied to vibrations double-walled carbon nanotubes (DWCNTs); specifically, evaluation natural frequencies achieved through Ru’s and He’s formulations. The actual discrete DWCNT modelled by means couple concentric equivalent continuous thin cylindrical shells, where Donnell shell theory adopted obtain strain-displacement relationships. order take into account chirality effect DWCNT, an anisotropic elastic model considered. Simply supported boundary conditions are imposed Rayleigh–Ritz method used approximate mode shapes. A parametric analysis considering values diameters numbers waves along longitudinal circumferential directions performed adopting From comparisons, it evident that formulation provides unsatisfactory results for relatively low high with respect more accurate formulation. This behaviour observed every number half-waves. Therefore, cannot be vibration modelling DWCNTs in large range wavenumbers.