Calculations of Static Equilibrium, Stability, and Vibrations of a Carbon Nanotube Based on the Moment-Membrane Theory of Elastic Thin Cylindrical Shells

As demonstrated by both experimental results and numerical modeling, elastic carbon nanotubes have proven to be remarkably strong materials, both in tension and bending. The discovered and other remarkable mechanical properties of single-walled carbon nanotubes open up promising opportunities for various important applications. The analysis of a single-walled carbon nanotube presents a complex problem, the solution of which should be grounded in continuum theories that take into account its discrete (crystalline) structure. The previously developed moment-membrane theory of elastic shells, particularly cylindrical shells, fully meets the above requirements. This theory offers extensive possibilities for investigating a wide range of mechanical problems related to single-walled carbon nanotubes. In this work, various equilibrium problems of a single-walled carbon nanotube are studied based on the moment-membrane theory of cylindrical shells. Problems concerning the static stability of the initial momentless state of the nanotube are also investigated (with respect to both critical force and distributed critical surface load), as well as problems related to the free vibrations of the nanotube (revealing that the lowest vibration frequencies lie in the terahertz range). All the problems considered are carried through to specific numerical results.