Analysis of Pull-in Characteristics of Double-clamped Nanobeam Incorporating Casimir and van der Waals Effects

A hybrid numerical scheme comprising the differential transformation method (DTM) and the finite difference (FD) approximation approach is used to analyze the complex nonlinear pull-in behavior of an electrostatically actuated double-clamped nanobeam subject to Casimir and van der Waals force effects and an axial residual stress. It is shown that, for an initial gap size of 50 nm, the pull-in voltage predicted by the hybrid numerical scheme deviates from that predicted by the universal pull-in formula by just 0.2%. In addition, the results show that the Casimir and van der Waals forces both have a significant effect on the steady and dynamic deflection behaviors of the beam as a function of applied voltage. Finally, the minimum allowable gap without the applied voltage of double-clamped nanobeams can be determined.