Nonlinear Response of CNT Cantilever Based Nano-Resonators

This paper presents nonlinear dynamic response of carbon nanotube (CNT) cantilevers incorporating electrostatic forces and van der Waals interactions between the CNT and the conducting plane. The CNT cantilever models including geometric and inertial nonlinearities for predicting unexpected phenomena when the deflection of the CNT is increased. As a result, the CNT cantilever shows complex dynamic responses due to the applied voltage. At the low voltages, the cantilever has only linear response at fundamental resonance except the superharmonic response due to the harmonic excitation of electrostatic field. The secondary resonance response branches off through period-doubling (PD) bifurcation, and becomes softened through saddle-node (SN) bifurcation when the applied voltage is increased. After SN bifurcation, the lower branch of the solution near resonance loses its stability and becomes unstable. This theoretical finding can help the prediction of complex response of the nano-resonators.