Nonlocal material properties of single-walled carbon nanotubes

Natural frequencies of single-walled carbon nanotubes (SWCNTs) obtained using a model based on Eringen's nonlocal continuum mechanics and the Timoshenko beam theory are compared with those obtained by molecular dynamics simulations. The goal was to determine the values of the material constant, considered here as a nonlocal property, as a function of the length and the diameter of SWCNTs. The present approach has the advantage of eliminating the SWCNT thickness from the computations. A sensitivity analysis of natural frequencies to changes in the nonlocal material constant is also carried out and it shows that the influence of the nonlocal effects decreases with an increase in the SWCNT dimensions. The matching of natural frequencies shows that the nonlocal material constant varies with the natural frequency and the SWCNT length and diameter.