Coupled Effect of Surface Energy and Size Effect on the Static and Dynamic Pull-In Instability of Narrow Nano-Switches

In this paper, the generalized differential quadrature (GDQ) method is employed to investigate the static and dynamic pull-in instability of nano-switches with small width/height ratio. For nano-switches with slender narrow-width beam elements, the corrections due to surface layer, external forces and size effect are crucial. So the couple-stress theory combined with the Gurtin–Murdoch surface elasticity is employed to incorporate the coupled effects of size phenomena and surface energy. In addition, the model accounts for the external force corrections by incorporating the impact of narrow width on the distribution of Casimir attraction, van der Waals force and the fringing field. The effects of the above-mentioned corrections on the static and dynamic pull-in parameters are demonstrated. The results from the modified model are compared with those from conventional parallel beam-plate models in the literature. It is shown that the corrections significantly affect the pull-in parameters of the narrow-width switches and hence, cannot be ignored in theoretical models. For wide switches, the results of the proposed model approach to those of the conventional models.