Applicability and Limitations of Simplified Elastic Shell Theories for Vibration Modelling of Double-Walled Carbon Nanotubes

The applicability and limitations of simplified models thin elastic circular cylindrical shells for linear vibrations double-walled carbon nanotubes (DWCNTs) are considered. models, which based on the assumptions membrane moment approximate thin-shell theories, compared with extended Sanders–Koiter shell theory. Actual discrete DWCNTs modelled by means couples concentric equivalent continuous thin, shells. Van der Waals interaction forces between layers taken into account adopting He’s model. Simply supported free–free boundary conditions applied. Rayleigh–Ritz method is considered to obtain natural frequencies mode shapes. Different aspect thickness ratios, numbers waves along longitudinal circumferential directions, analysed. In cases axisymmetric beam-like modes, it proven that theory, differently from provides results excellent agreement On other hand, in case shell-like found both theories provide reporting acceptable theory only very limited ranges geometries wavenumbers. Conversely, modes a newly developed, model, combination semi-moment satisfactory all ranges.