Using strain gradient elasticity in conjunction with Gurtin–Murdoch theory for modeling the coupled effects of surface and size phenomena on the instability of narrow nano-switch

While comprehensive researches have been conducted on modeling the electromechanical stability of wide-enough beam-plate nano-switches, few researchers have focused on modeling the electromechanical instability of narrow-width nano-switches. For such systems, considering the coupled effects of surface stresses and size dependency of material characteristics is crucial as well as applying appropriate force models. In this paper, Gurtin–Murdoch surface theory incorporating with strain gradient elasticity is employed to study the pull-in instability of narrow-width beam-type nano-switch with small width to height ratio. The model accounts for the force corrections, i.e. the impact of finite dimensions on the fringing field, Casimir attraction and van der Waals force. Furthermore, a modified gas damping model has been incorporated in the governing equation. The nonlinear governing equation was solved using analytical Rayleigh–Ritz method. The influences of the above-mentioned corrections on the static and dynamic pull-in parameters, phase planes and stability threshold of the switch are demonstrated. The modified model is compared with conventional parallel beam-plate models in the literature.