A numerical-analytical methodology for acquiring the electrical force of carbon nanotube–based nanoactuator assuming an out-of-plane electrodes arrangement

In this paper, we develop a simple expression to evaluate the electric force acting on a carbon nanotube–(CNT) based nanoactuator assuming a nonparallel actuating plates (out-of-plane) arrangement. The actuating force is initiated by the asymmetry of the resultant electric fringing fields caused mainly due to the nonparallel electrodes arrangement. The nanoactuator is designed based on a CNT flexible electrode (nonstationary) and 2 symmetrically located actuating stationary rectangular shaped out-of-plane plates. The resultant electric force is mathematically approximated from the outcomes of a planar (2-D) numerical solution of the electric problem via a finite element–based numerical analysis. The influence of the design geometrical parameters on the resultant electric force are examined. Several key design parameters were inspected: the width and thickness of the stationary actuating electrodes, the radius of the flexible electrode (the CNT), and the lateral and vertical separation distances between the movable and grounded electrodes. Through several simulations, we show the effect of the lateral and vertical offsets as well as the electrodes thickness in the optimization of the performance of the nanoactuator assuming such nonparallel plates actuating configuration. We also simulate the effect on the resultant actuating force level with the electrode thickness as well as the electrodes lateral separation distance.