Multistability in an electrically actuated carbon nanotube: a dynamical integrity perspective

This study deals with a slacked carbon nanotube, which is electrostatically and electrodynamically actuated. After introducing a reduced-order model, we investigate the overall scenario of the device response when both the frequency and the electrodynamic voltage are varied. Extensive numerical simulations are performed. The nanostructure exhibits several competing attractors with different characteristics. We examine the multistability in detail, based on numerical integration of the equation of motion in time, since it leads to a considerable versatility of behavior, which may be desirable in applications. Nevertheless, these results do not take into account the presence of disturbances, which are unavoidable under realistic conditions. To extend them to the practical case where disturbances exist, we develop a dynamical integrity analysis. This is performed via the combined use of several dynamical integrity tools. Analyzing the potential well, we observe that the device may be vulnerable to pull-in considerably before the theoretical inevitable escape. Focusing on the safe range, the main attractors are examined to investigate the practical probability to catch them and the practical disappearance of the main ones. Special attention is devoted to the practical final response, to detect where the safe jump to another attractor may be ensured and where instead dynamic pull-in may arise. We build the integrity charts, which are able to illustrate if and in which parameter range the theoretical predictions can be guaranteed in practice. They may be used to establish safety factors to effectively operate the device according to the desired outcome, depending on the expected disturbances.