Model and behaviour of forced double-walled nanotube oscillators

Abstract

In this paper we present a model for gigahertz oscillators comprising two coaxial carbon nanotubes of which the outer tube is xed and the inner tube is allowed to freely oscillate due to the in uences of van der Waals interactions and a sinusoidal forcing term. We examine the oscillatory behaviour predicted by the model, including the in uence of forcing field strength and frequency. Neglecting dissipative terms and thermal effects we derive a model which may be solved analytically, region by region, which we use to evolve numerical results for the model, obviating the need to use a numerical ODE solving algorithm. The results for this model show that the induced amplitude and frequency of oscillation are both functions of the forcing field strength and forcing frequency. In the dominant regime, increasing forcing frequency leads to decreasing induced amplitude and increase eld strength generally leads to a decrease in the frequency in the principle mode of induced oscillation. We also note that the device can lead to highly ordered behaviour for very special initial condition and forcing parameters. However, we nd that small perturbation to these initial conditions may destroy the ordered behaviour.