Modeling the nonlinear pull-in behavior of tunable nano-switches

Double-sided nano-devices can potentially be used as tuning switches and variable capacitors. In this paper, the pull-in behavior of double-sided cantilever nano-wires, including the Casimir and partial electrostatic attractions are developed. To increase the tunability, only a piece of substrate plates is electrostatically actuated and conductors' voltage can be different. Herein, the governing nonlinear equation is derived via extended Hamilton's principle. The Galerkin method is used to discretize the differential EOM and the step-by-step linearization method is employed to solve them numerically. The validity of the presented model is confirmed by comparing the theoretical results with the experimental reported ones. The influence of geometrical parameters, i.e. stationary electrodes distance (initial gaps), non-actuated piece length/location as well as wire diameter and length on the instability is investigated. Furthermore, the effect of surface elasticity, residual surface tension and length-scale on the free vibration is examined. It is concluded that the geometric configuration characteristics play significant roles in the pull-in deflection and voltage of nano-structures, which should be considered in applying design and tuning applications.