Numerical Analysis of Nanotube Based NEMS Devices — Part II: Role of Finite Kinematics, Stretching and Charge Concentrations

In this paper a nonlinear analysis of nanotube based nano-electromechanical systems is reported. Assuming continuum mechanics, the complete nonlinear equation of the elastic line of the nanotube is derived and then numerically solved. In particular, we study singly and doubly clamped nanotubes under electrostatic actuation. The analysis emphasizes the importance of nonlinear kinematics effects in the prediction of the pull-in voltage of the device, a key design parameter. Moreover, the nonlinear behavior associated with finite kinematics (i.e., large deformations), neglected in previous studies, as well as charge concentrations at the tip of singly clamped nanotubes, are investigated in detail. We show that nonlinear kinematics results in an important increase in the pull-in voltage of doubly clamped nanotube devices, but that it is negligible in the case of singly clamped devices. Likewise, we demonstrate that charge concentration at the tip of singly clamped devices results in a significant reduction in pull-in voltage. By comparing numerical results to analytical predictions, closed form formulas are verified. These formulas provide a guide on the effect of the various geometrical variables and insight into the design of novel devices.