Static and Dynamic Pull-in Instabilities Analysis of Partially Affected Clamped Nano Actuators: The Substrate Effect

Many researches have been carried out for modeling of micro/nano electromechanical systems instabilities, in which both movable and substrate electrodes are at the same size; however, there is no research considering the static and dynamic pull-in instabilities of micro/nano actuators with a smaller substrate electrode in the presence of small size effects. In the present study, the static and dynamic behaviors of partially affected clamped micro/nano actuators are investigated and the effects of position and length of the substrate electrode are analyzed. The non-linear Euler-Bernoulli governing equation of the beam motion and the corresponding boundary conditions are derived using the Modified couple stress theory. Finite element method is utilized to solve the governing equations. In order to investigate the accuracy of the utilized finite element method, the obtained results are compared with those available in the literature and a good agreement between them was found. The results demonstrate that a decrease of the substrate electrode length leads to an increase of the required pull-in voltage and the pull-in capillary force. Moreover, a small reduction in the pull-in deflection of the nano-beam is observed because of the decrease of the substrate electrode. Finally, a new parameter, named as balanced size effect-capillary force which changes the trend of the behavior of the nano-beam, is introduced.