Investigation of nonlinear dynamic behavior of a capacitive carbon nano-tube based electromechanical switch considering van der Waals force

Abstract

In this study, nonlinear dynamic behavior of a capacitive carbon nano-tube switch is investigated considering van der Waals (vdW) force. The carbon nano-tube is considered as a nano-beam and dynamic equation of motion for this switch is presented based on the Euler–Bernoulli beam model. In order to simplify the bifurcation analysis of the carbon nano-switch, dynamic equation based on the modified mass–damper–spring model has been extracted. The fixed points of the switch have been studied in the absence and presence of the electrostatic force. Global and local criterion for stability study of the nano switch is employed. In order to study the local stability of the fixed points, the associated eigenvalues were extracted and the stability of these points was identified. For studying global stability, motion trajectories of the switch with and without considering damping effect are provided and presented. Basin of attraction set and region of periodic set and dependency of them on the applied voltage, as well as the vdW force and damping effect are investigated. Critical values of the applied voltage and vdW parameter leading to qualitative changes in the nano switch behavior through a saddle node bifurcation are obtained.