Fractal Pull-in Stability Theory for Microelectromechanical Systems

Abstract

Pull-in instability was an important phenomenon in microelectromechanical systems (MEMS). In the past, MEMS were usually assumed to work in an ideal environment. But in the real circumstances, MEMS often work in dust-filled air, which is equivalent to working in porous media, that's mean fractal space. In this paper, we studied MEMS in fractal space and established the corresponding model. At the same time, we can control the occurrence time and stable time of pull-in by adjusting the value of the fractal index, and obtain a stable pull-in phenomenon.

Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller

“…15 The inherent pull-in instability of MEMS systems can be completely overcome by the fractal vibration theory. [16][17][18] The homotopy perturbation method (HPM) 19 and the Hamitonian approach 20 are two main analytical tools for nonlinear vibration systems. The combination of the Laplace transforms, Lagrange multiplier, fractional complex transforms, and Mohand transform with HPM was employed to find approximate solutions for nonlinear partial differential equations.…”

Study on the nonlinear vibration of embedded carbon nanotube via the Hamiltonian-based method

“…Recently, He's frequency formulation, which is first proposed by Chinese mathematician Ji-Huan He, has been widely used to solve the nonlinear vibrations arising in three-dimensional printing technology, 25 micro-electromechanical, 26 N/MEMS, 27 and so on . 28,29 By using He's frequency formulation, we can get the frequency-amplitude formulation of equation (1.1) as…”

A simplified He’s frequency–amplitude formulation for nonlinear oscillators

“…which has been used in many previous works. [36][37][38][39][40][41][42][43][44][45][46][47][48] In the light of the t 4 terms, we will have…”