Fractal N/Mems: From Pull-in Instability to Pull-in Stability

Abstract

Pull-in instability, as an inherent nonlinear problem, continues to become an increasingly important and interesting topic in the design of electrostatic Nano/Micro-electromechanical systems (N/MEMS) devices. Generally, the pull-in instability was studied in a continuous space, but when the electronic devices work in a porous medium, they need to be analyzed in a fractal partner. In this paper, we establish a fractal model for N/MEMS, and find a pull-in stability plateau, which can be controlled by the porous structure, and the pull-in instability can be finally converted to a stable condition. As a result, the pull-in instability can be completely eliminated, realizing the transformation of pull-in instability into pull-in stability.

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…”

He’s frequency formula to fractal undamped Duffing equation

“…Due to the shortness of finding exact solutions, these nonlinear equations are extremely imperative to be solved by employing analytical and numerical methods, for example, the variational iteration method, [11][12][13] the homotopy perturbation method, 14 the Hamiltonian approach, 15,16 and the Taylor series method. [17][18][19] Fractal calculus especially provides a powerful tool for characterizing the mechanical behavior of a nonlinear oscillator in a fractal space, [20][21][22][23][24][25][26][27] which cannot be revealed by the classical differential models. For examples, some interesting properties of the fractal Toda oscillator was first revealed, 20 Fangzhu's passive water harvesting was explored using a fractal oscillation model, [21][22][23][24][25] the fractal MEMS oscillator can eliminate the pull-in instability, 26 which is an intrinsic property of the traditional MEMS oscillator.…”

“…[17][18][19] Fractal calculus especially provides a powerful tool for characterizing the mechanical behavior of a nonlinear oscillator in a fractal space, [20][21][22][23][24][25][26][27] which cannot be revealed by the classical differential models. For examples, some interesting properties of the fractal Toda oscillator was first revealed, 20 Fangzhu's passive water harvesting was explored using a fractal oscillation model, [21][22][23][24][25] the fractal MEMS oscillator can eliminate the pull-in instability, 26 which is an intrinsic property of the traditional MEMS oscillator. The fractional Schrodinger equation, 9 the fractional Camassa-Holm equation, 9 and the fractional Kundu-Mukherjee-Naskar equation 27 also showed plenty of solution properties.…”