A Robust Hybrid Solution for Pull-in Instability of FG Nano Electro-Mechanical Switches Based on Surface Elasticity Theory

The precise computation of nanoelectromechanical switches’ (NEMS) multi-physical interactions requires advanced numerical models and is a crucial part of the development of micro- and nano-systems. This paper presents a novel compound numerical method to study the instability of a functionally graded (FG) beam-type NEMS, considering surface elasticity effects as stated by Gurtin-Murdoch theory in an Euler-Bernoulli beam. The presented method is based on a combination of the Method of Adjoints (MoA) together with the Bézier-based multi-step technique. By utilizing the MoA, a boundary value problem (BVP) is turned into an initial value problem (IVP). The resulting IVP is then solved by employing a cost-efficient multi-step process. It is demonstrated that the mentioned method can arrive at a high level of accuracy. Furthermore, it is revealed that the stability of the presented methodology is far better than that of other common multi-step methods, such as Adams-Bashforth, particularly at higher step sizes. Finally, the effects of axially functionally graded (FG) properties on the pull-in phenomenon and the main design parameters of NEMS, including the detachment length, are inspected. It was shown that the main parameter of design is the modulus of elasticity of the material, as Silver (Ag), which had better mechanical properties, showed almost a 6% improvement compared to aluminum (Al). However, by applying the correct amount of material with sturdier surface parameters, such as Aluminum (Al), at certain points, the nanobeams’ functionality can be improved even further by around 1.5%.