Nonlinear oscillations of a double-walled carbon nanotube

An elastic continuum approach for modeling the nonlinear vibration of a double-walled carbon nanotubes under harmonic excitation is presented. The carbon nanotube is modeled as two doubly clamped beams coupled through nonlinear continuous springs representing van der Waal bonds. Geometric nonlinearity is included due to mid-plane stretching. A Galerkin approach is used to discretize the integro-partial differential equation leading to two nonlinear coupled second-order ordinary differential governing equations. The numerically obtained dynamic response to a primary-resonance exciting the co-axially first and second vibration modes is investigated through frequency response, periodic and chaotic motions characteristics.