Using couple stress theory for modeling the size-dependent instability of double-sided beam-type nanoactuators in the presence of Casimir force

While the pull-in instability of beam-type electromechanical nanoactuators with single actuating electrode has been widely addressed in literature, limited research works have been devoted to modeling the pull-in phenomenon in actuators with double-sided actuating electrodes. Herein, couple stress theory (CST) has been used to study the size-dependent instability of two double-sided actuators, i.e., nano-bridges and nano-cantilevers. The influence of Casimir force has been considered in the model. The analytical differential transformation method (DTM) has been applied to solve the governing equations as well as numerical method. Furthermore, a lumped parameter model has been developed to simply explain the physical performance of the systems without mathematical complexity. The critical deflection and pull-in voltage of the nanostructures as basic design parameters have been calculated. Effect of the Casimir attraction and the size dependency and the importance of coupling between them on the pull-in performance have been discussed for both nano-structures. The present work can be helpful to precise design and analysis of nano-cantilevers and nano-bridges.