Pull-in Stability of a Fractal Mems System and Its Pull-in Plateau

Abstract

The pull-in instability is the inherent property of a micro-electromechanical system (MEMS) when the voltage is larger than its threshold value. Recently, a fractal MEMS system was proposed to overcome the pull-in instability with great success, and it has opened a total new path for the so-called pull-in stability. This paper suggests a pull-in plateau, a novel concept for qualifying the pull-in stability. The plateau’s basic properties are elucidated, and the effect of the fractal dimensions on the plateau width is elucidated, and the paper concludes that there exists a critical condition for an ever pull-in stability when both the acceleration and the speed of the system equal zero.

Pull-down plateau of a Toda-like fractal-fractional oscillator and its application in grass carp’s roes’ agglomeration

“…Professor Ji-Huan He and his students proposed a novel concept for qualifying the pull-in stability, which is called as He's pull-in plateau. 23 Also, the pull-down instability of a quadratic nonlinear oscillator was suggested by He and coworkers. 7 Applying the ideas directly from Refs.…”

“…7 Applying the ideas directly from Refs. [7] and [23] we study He's pull-down plateau of the Toda-like fractalfractional oscillator to illustrate the roes' agglomeration. Firstly, the previous work on He's pull-in plateau of the fractal MEMS oscillator was presented in Ref.…”

“…This concept of the pull-in stability was first proposed in Ref. [23]. Along with the pull-in phenomenon has become increasingly important, similar instability characteristics of nonlinear systems have also begun to be studied.…”

Dynamic behaviors for the graphene nano/microelectromechanical system in a fractal space

“…There are various methods in the literature to deal with the pull-in instability: Anjum et al 10 gave a systematical review on various analytical methods for MEMS systems, Anjum et al 11 showed that the variational iteration method is an efficient tool to the analysis of the periodicity of an N/MEMS, Ji-Huan He et al established a variational theory for MEMS systems, 12 Anjum et al applied Li-He's modification of the homotopy perturbation method with great success, 13 Rehman et al suggested a modified variational iteration method coupled with Laplace transform, 14 and Ji-Huan He et al discovered the pull-in plateau. 15 Carbon-based nanomaterials, including one-dimensional carbon nanotubes (CNTs) and two-dimensional graphene, 16,17 are more attractive in various N/MEMS applications (such as electronic components, mass/gas sensors, and supercapacitors) due to their unique mechanical, electrical, optical, and chemical properties and have become the first choice for sensing applications in MEMS (microelectromechanical systems) and NEMS (nanoelectromechanical systems) devices. [18][19][20][21][22] Graphene is widely used in mass and gas sensing applications because of its low mass and high surface to volume ratio and its good mechanical and electronic properties.…”

“…There are various methods in the literature to deal with the pull-in instability: Anjum et al 10 gave a systematical review on various analytical methods for MEMS systems, Anjum et al 11 showed that the variational iteration method is an efficient tool to the analysis of the periodicity of an N/MEMS, Ji-Huan He et al established a variational theory for MEMS systems, 12 Anjum et al applied Li-He’s modification of the homotopy perturbation method with great success, 13 Rehman et al suggested a modified variational iteration method coupled with Laplace transform, 14 and Ji-Huan He et al discovered the pull-in plateau. 15…”