ï»¿A nonlinear pull-in behavior analysis of a cantilever nano-actuator was carried out and an Eulerâ€“Bernoulli beam model was used in the examination of the fringing field and the surface and Casimir force effects in this study. In general, the analysis of an electrostatic device is difficult and usually complicated by nonlinear electrostatic forces and the Casimir force at the nanoscale. The nonlinear governing equation of a cantilever nano-beam can be solved using a hybrid computational scheme comprising differential transformation and finite difference to overcome the nonlinear electrostatic coupling phenomenon. The feasibility of the method presented here, as applied to the nonlinear electrostatic behavior of a cantilever nano-actuator, was analyzed. The numerical results for the pull-in voltage were found to be in good agreement with previously published results. The analysis showed that the surface effects had significant influence on the dynamic characteristics of the cantilever nano-actuator. 
Surface effect on dynamic characteristics of the electrostatically nano-beam actuator