Analysis of nonlinear oscillation of circular curved carbon nanotube

The nonlinear vibration of a circular curved carbon nanotube using Euler-Bernoulli beam theory is investigated. The governing equation of motion of the system is developed and the Galerkin method is utilized to obtain the nonlinear ordinary differential equation of the curved carbon nanotube. A quarter-circular curvature is considered for the nanotube and it is assumed to have a single wall with simply-supported boundary conditions. Two semi analytical approaches to study the behavior of the developed nonlinear differential equation are utilized and the frequency-amplitude relationship of the objective system is obtained. Subsequently, a parametric study is performed to study the importance of different parameters, such as the amplitude of oscillation and the curvature radius, on the nonlinear behavior of the system. Finally, numerical simulation is carried out to obtain the results and investigate the accuracy of the analytical solution methods applied.