Nonlinear elastic shell model for carbon nanotube oscillations

Nonlinear model of single-walled nanotube geometrically nonlinear oscillations is derived. The Sanders-Koiter nonlinear shell theory accounting nonlocal elasticity is basis of this model. The system of the partially differential equations of the nanotube nonlinear oscillations is obtained. The system of nonlinear ordinary differential equations for the nanotube oscillations is derived using Galerkin technique. The backbone curves of free nonlinear oscillations are calculated.