Voltage Response of Parametric Resonance of Double Wall Carbon Nanotube Under Electrostatic Actuation

In this paper, the Method of Multiple Scales is used to investigate the influences of damping and detuning frequency parameters on the amplitude-voltage response of an electrostatically actuated double-walled carbon nanotube. The forces responsible for the nonlinearities in the vibrational behavior are intertube van der Waals and electrostatic forces. Herein, the coaxial case is investigated, which eliminates the influence of the cubic van der Waals in the first-order solution. The double-walled carbon nanotube structure is modelled as a cantilever beam with Euler-Bernoulli beam assumptions since the double-walled carbon nanotube is characterized with high length-diameter ratio. The results shown assume steady-state solutions in the first-order Method of Multiple Scales solution. The importance of the results in this paper are the effect of damping and detuning frequency on the Hopf bifurcations, as these define the intervals of voltage for nonzero amplitudes.