Study On The Nonlinear Dynamic Of Carbon Nanotube And Nanobeam Under The Voltage Excitation

Carbon nanomaterials have some properties, such as high flexibility, low density,good insulation and high strength. These special properties can be widely used in nano devices, sensors and nano machinery. Therefore, the studying of the dynamic characteristics of carbon nanotube and nanobeam is very meaningful.Respectively, with charging carbon nanotube and nanobeam of rectangular and circular cross-sectional under the voltage excitation as objects, according to the Lagrange function, the nonlinear dynamic equation of carbon nanobeam and nanotube system is established. The nonlinear vibration analysis through the multiple scales method and the MLP method is made.1) Using the multiple scales method to researching on carbon nanobeam and nanotube is affected by voltage. The results show that with the increase of the length and AC voltage of the carbon nanobeam, the amplitude and the resonance region of the response curves enlarge. With the increase of the spacing of the nanobeam and fixed plate, damping coefficient, the amplitude and the resonance region of the response curves decrease. With the increase of carbon nanotube length and AC voltage, the amplitude and the unstable interval become larger. With the increase of carbon nanotube radius and plate distance, the amplitude and the unstable interval become smaller, whenσis close to zero, the amplitude of the response curves hardly changes with the other system parameters.2) Using the MLP method to research on rectangular cross-section of carbon nanobeam is affected by voltage about strong nonlinear vibration problem. The results show that with the increase of the length and AC voltage of the carbon nanobeam, the amplitude and the resonance region of the response curves enlarge. With the increase of the spacing of the nanobeam and fixed plate, the amplitude and the resonance region of the response curves decrease.