Weak solution of longitudinal waves in carbon nanotubes

This paper studies weak solutions of the axial oscillations of the carbon nanotube modeled as an elastic nanobeam surrounded by an elastic medium. The model used combines Eringen’s theory of non-local elasticity and the equations of axial oscillations proposed by Aydogdu. Based on the Sturm–Liouville problem associated with this case, the weak solutions of the longitudinal waves in the carbon nanotube are determined.