Higher order nonlocal strain gradient approach for wave characteristics of carbon nanorod

In this paper an attempt is made to study the wave dispersion characteristics of a carbon nanorod through second, fourth, sixth and eighth order nonlocal strain gradient models. Expressions are derived for both wave number and wave speeds of the nanorod. The wave characteristics of the nanorod obtained from the nonlocal strain gradient models are compared with the classical continuum model. From these models it is observed that sixth order strain gradient model gives the better approximation than the second and fourth order strain gradient models for dynamic analysis. The second and sixth order strain gradient models gave critical wave number at a certain wave frequency, which does not exist in fourth and eight order strain gradient models.