A Hybrid Numerical Study of the Nonlinear Instability of Nano-switches

This study offers a computationally efficient technique to study the pull-in instability phenomenon of beam-type nano-switches using nonlocal elasticity theory. The governing equation of the system is derived using the Hamilton principle based on the Timoshenko beam theory. A hybrid combination of the method of adjoints (MoA) with the Bezier-based multistep technique is utilized to obtain the solution for the instability pull-in voltage. The MoA is firstly used to convert the governing nonlinear boundary value problem (BVP) of the micro-switch to the corresponding initial value problem (IVP). Then, the resulted IVP system is solved using the robust Bézier procedure. Results of the presented hybrid solution are compared with other well-known methods such as Adams-Bashforth, Taylor, and Runge-Kutta methods. Results revealed that for higher step sizes, the presented method provides more stable results in comparison with other techniques. This study presents a framework, similar to shooting method, for converting a general nonlinear BVP to an IVP system, which can be solved using various analytical and numerical methods. Finally, a parametric study is provided to investigate the effects of size dependency, shear effects, and intermolecular forces on the static behavior of nano-switch and instability voltage.