Resonant pull-in of a double-sided driven nanotube-based electromechanical resonator

We theoretically investigate the electromechanical dynamics of a double-sided driven cantilevered nanotube-based electromechanical resonator. Closed-form analytical solutions capable of predicting the steady-state resonant oscillation of the device and its resonant pull-in conditions are derived using an energy-based method and are verified through a comparison with numerical simulations. Our closed-form formulas clearly reveal the complex relationship among the device geometry, driving voltages, and the device's electromechanical dynamics. Our results show that the stable steady-state spanning range of the resonating cantilever can reach up to 90% of the gap between the actuation electrodes, which substantially exceeds the previously reported quasistatic pull-in limit for cantilevered nanotube-based nanoelectromechanical systems and the resonant pull-in limit for double-sided driven microelectromechanical gyroscopes. Our results also reveal that the processes of tuning the resonant frequency of the resonator and controlling its stable steady-state oscillation amplitude can be decoupled and controlled separately by controlling the dc and ac components in the driving signal. The unique behavior of the large stable steady-state resonant oscillation range, which is independent of the electrostatic-force-induced resonant frequency tuning, makes this double-sided driven resonator attractive for many applications, such as tunable sensors for detecting ultratiny mass and force and tunable electronics. The results reported in this paper are useful to the optimal design of novel nanotube- or nanowire-based double-sided driven electromechanical resonators.