Nonlinear vibration of single walled carbon nanotube resonators

Abstract

Since their discovery in 1991, carbon nanotubes (CNT) have been recognized to be ideal components for a wealth of technological applications. Vibrations of carbon nanotubes are of considerable importance in a number of miniaturized devices such as oscillators, charge detectors, clocks, emission devices and sensors. This thesis presents a general study of nonlinear vibration of a single-walled carbon nanotube, which is doubly-clamped at a source and a drain. The carbon nanotube is excited harmonically by an electrostatic force. The problem is modeled in the context of an elastic continuum beam theory, involving a mid-plane stretching and phenomenological damping. The dynamic response of the nanobeam shows a sequence of period-doubling bifurcations leading to chaos where the carbon nanotube is assumed to be perfectly straight. Moreover, the model is extended to involve a curved single-walled carbon Nanotube, which is taken into account according to the strong evidence of existence of waviness in CNTs. The dynamic response of this case is simulated and showed a sequence of period doubling bifurcation culminating to chaos. This case is suggested to be more realistic to model the vibration of the carbon nanotube in comparison to the earlier case.