Noncoaxial Vibration of Electrostatically Actuated DWCNT: Frequency Response of Primary Resonance

In this paper, the Method of Multiple Scales (MMS) is used to investigate the influences of the nonlinear intertube van der Waals coefficient, dimensionless damping, and voltage on the amplitude-frequency response of an electrostatically actuated double-walled carbon nanotube (DWCNT). The forces responsible for the nonlinearities in the vibrational behavior are intertube van der Waals and electrostatic forces. For perturbation, a small viscous damping and soft AC actuation are assumed for numerical simulation. For the first time in literature, forced vibration of the noncoaxial (out-of-phase) case is investigated. In this mode of vibration, the outer and inner carbon nanotubes move at ultra-high frequency in opposite direction, i.e., negative amplitude ratio. The DWCNT structure is modelled as a cantilever beam with Euler-Bernoulli beam assumptions since the DWCNT is assumed to have a high length-diameter ratio. The results shown assume steady-state solutions in the second-order MMS solution. The importance of the results in this paper are the effect of the strong nonlinearity of the van der Waals coefficient, damping, and voltage on the the DWCNT vibration.