Vibration analysis of embedded curved carbon nanotube subjected to a moving harmonic load based on nonlocal theory

Abstract

In the present study, forced vibration of a simply supported embedded curved single-walled carbon nanotube (ECSWCNT) subjected to a moving harmonic load is investigated based on nonlocal Euler-Bernoulli beam theory. By using a single-mode Galerkin approximation method, the nonlinear integral-differential equation governing the motion of the nanotube is converted into a second-order nonlinear ordinary differential equation. The differential equation of the model is solved using Magnus expansion method which is one of the geometric integration methods. In the numerical calculation, the effects of nonlocal parameter, aspect ratio of ECSWCNT, velocity and the elastic medium constant is discussed. The results show that the above mentioned effects play an important role on the dynamic behavior of ECSWCNT.