Pull-in-free design of electrically actuated carbon nanotube-based NEMS actuator assuming non-parallel electrodes arrangement

In this numerical investigation, the nonlinear structural response of an electrostatic carbon nanotube (CNT) based nano-actuator assuming a non-parallel (out-of-plane) plates actuation configuration is examined. The actuating force is initiated by the asymmetry of the resultant electric fringing-fields caused mainly due to the non-parallel electrodes scheme. The nano-actuator is designed based on a carbon nanotube flexible moving electrode and two symmetrically located actuating stationary rectangular-shaped out-of-plane electrodes. First, the electrical problem of the nano-actuator is numerically solved to acquire the resultant actuating force. The force is then mathematically approximated from the outcomes of a 2D numerical solution of the electric problem via a finite-element-based numerical analysis. Then, the structural behavior of the CNT-based nano-actuator under the effect the resultant non-parallel electric fields is investigated numerically via a modal expansion process. The electro-mechanical model was constructed based on an Euler–Bernoulli continuous nonlinear beam model, where both the mid-plane stretching (geometric nonlinearity) and the electric non-parallel fringing-fields effects have been taken into consideration. The reduced-order model (ROM) was derived using the Galerkin decomposition via modal decomposition process. The resultant nonlinear equations are solved numerically to get the static response of the considered CNT-based nano-actuator for various DC voltages. The eigenvalue problem is afterward derived and studied to get the variation of the fundamental as well as higher-order natural frequencies when the system is deflected by a non-zero DC amplitude. A detailed parametric study indicates an opportunity of having larger stroke as well as higher fundamental natural frequency for such CNT-based nano-actuator function of the assumed DC voltage amplitude, enabling it to be used as a tunable NEMS-based device without any pull-in scenario.