Static and Dynamic Pull-in Phenomena of a Capacitive Carbon Nano Tube

In this paper, static and dynamic responses of a Double Walled Carbon Nano Tube (DWNT) switch subjected to electrostatic force and considering van der Waals (vdW) force have been studied. Governing formulas for electrostatic and vdW forces have been presented. Because of complication of these relations, they have been simplified with considering approvable conditions. Hence the obtained nonlinear equations for tatic and dynamic behaviors of a DWNT have been presented. Due to the nonlinearity of electrostatic and vdW forces, the analytical solutions for the presented equations are not available so the obtained differential equation for static case has been linearized using step by step linearization method (SSLM) and obtained linearized equation has been discretized using Galerkin weighted residual method. Dynamic response have been studied using linearized form of Galerkin based reduced order model and nonlinear forcing terms have been accounted using an iteration procedure. The corrections of obtained equations and numerical methods have been validated with previous works. In results section, it has been shown that the effects of vdW force for some orders of properties has more significant and with increasing this effects the corresponding static pull-in voltage decreases and for detachment case it has been shown with increasing initial gap and Young modulus corresponding detachment length increase too. Dynamic response of a DWNT switch to a stepwise DC voltage excitation at the presence of vdW force has been investigated. The results show that the ratio of undamped dynamic to static pull-in voltage is a certain value and with decreasing primary gap of switch thisamount rises to finite magnitude. By considering damping effects pull-in voltage increases, this increase is continued up to a definite value of DC in which the nano beam tends to be critically damped and the dynamic pull-in voltage tends to be equal with the static one.

کلیدواژه ها:

CNT ، nems ، pull-in