Phonon dispersion analysis of carbon nanotubes based on inter-belt model and symplectic solution method

The objective of the study is to develop a totally new theory and structural mechanics model for phonon dispersion analysis of carbon nanotubes. The fundamental theory and computational algorithm for phonon dispersion analysis of carbon nanotubes are developed based on the symplectic theory and algorithm established in applied mechanics in recent years. Carbon nanotubes are simulated by two kinds of structural mechanics models, i.e. the conventional sub-structure model and the inter-belt model. The variational principle for wave dissipation analysis of periodic structure is given on the basis of the symplectic-mathematical theory. Numerical examples are carried out to demonstrate the validity of the theory and algorithm developed. By the comparison of the results obtained by the two kinds of structural mechanics models, it can be found that the inter-belt model has more advantages than the conventional sub-structure model in the calculation of phonon spectra of nanotubes. As a basic research work, the present study illustrates well the potential of the symplectic-mathematical theory as well as the inter-belt model and is valuable for the further research in computational nanomechanics.