NONLINEAR VIBRATION OF CARBON NANOTUBES RESONATOR UNDER PARAMETRIC EXCITATION

In this paper the nonlinear vibration response of doubly-clamped carbon nanotubes resonator under DC and AC harmonic excitation was investigated. Based on Euler Bernoulli beam theory the nonlinear governing equations was derived by the Hamilton’s principle, where the geometry nonlinear was considered and the nonlinear electrostatic force, van der Waals force and its initial static deformation were disregarded. The primary resonance of this system occurred when the excitation frequency was approaching to the natural frequency of the clamped-clamped carbon nanotubes. In this case, the reduced-order equations were scattered by Galerkin method and frequency response curves were obtained by perturbation method. Then, the effect of some parameters such as damping, DC load, AC harmonic load and geometric cubic nonlinear terms on the response of this system was discussed. The result shows that the geometrically cubic nonlinear terms has a great impact on the vibration response for carbon nanotubes resonator under external excitation. Furthermore carbon nanotubes has higher sensitivety and softening behavior to a certain extent under AC harmonic load comparing with DC load.