The analysis for the dynamic pull-in of a micro-electromechanical system

Feng, Guang-Qing; Niu, Jing-Yan

doi:10.1177/14613484221145588

Cited by 5 publications

(4 citation statements)

References 26 publications

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“…Similar to the results in the previous tables, the data are good for the period [0, 1]. Problem 4.7: We consider the following micro-electromechanical system (MEMS)[52]:y″ + y + θ y − 1 0, θ > 0, (4.46) with the ICs: y 0 ( ) y′ 0 ( ) 0. (4.47)…”

mentioning

confidence: 53%

“…At small values of θ, the solution of the system is stable and periodic, whereas at large values of θ, it becomes Frontiers in Physics frontiersin.org unstable, called pull-in instability. Figure 1 shows that the system is stable and periodic at θ values less than or equal to the critical value (θ 0.203632188) [52], and it becomes unstable at θ values greater than the critical one.…”

Section: (412)mentioning

confidence: 99%

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A modern analytic method to solve singular and non-singular linear and non-linear differential equations

El-Ajou,

Al-ghananeem,

Saadeh

et al. 2023

Front. Phys.

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This article circumvents the Laplace transform to provide an analytical solution in a power series form for singular, non-singular, linear, and non-linear ordinary differential equations. It introduces a new analytical approach, the Laplace residual power series, which provides a powerful tool for obtaining accurate analytical and numerical solutions to these equations. It demonstrates the new approach’s effectiveness, accuracy, and applicability in several ordinary differential equations problem. The proposed technique shows the possibility of finding exact solutions when a pattern to the series solution obtained exists; otherwise, only rough estimates can be given. To ensure the accuracy of the generated results, we use three types of errors: actual, relative, and residual error. We compare our results with exact solutions to the problems discussed. We conclude that the current method is simple, easy, and effective in solving non-linear differential equations, considering that the obtained approximate series solutions are in closed form for the actual results. Finally, we would like to point out that both symbolic and numerical quantities are calculated using Mathematica software.

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mentioning

confidence: 53%

Section: (412)mentioning

confidence: 99%

A modern analytic method to solve singular and non-singular linear and non-linear differential equations

El-Ajou,

Al-ghananeem,

Saadeh

et al. 2023

Front. Phys.

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show abstract

“…14 Yang studied a mathematical control for the pseudo-pull-in stability of the MEMS system. 15 Consider the MEMS oscillator as follows 16,17…”

Section: Introductionmentioning

confidence: 99%

“…Consider the MEMS oscillator as follows 16,17 where y and ρ are the dimensionless distance and voltage-related parameters, respectively.…”

Section: Introductionmentioning

confidence: 99%

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

Niu

2023

Journal of Low Frequency Noise, Vibration and Active Control

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Grass carp’s roes should be agglomerated together for maximizing their survival rate against various predators. Any vibration induced by any environmental perturbation should be attenuated immediately. A Toda-like fractal-fractional oscillator is established, which shows a low-frequency property for most cases; however, the grass carp has evolved a very ability to attenuate the perturbated vibration by sticky adhesion. The pull-down stability of the roes’ vibration is discovered through the results of phase diagrams. The mathematical analysis reveals that there is a pull-down plateau for the attenuating process, the plateau’s height and width are discussed graphically, and the main factors affecting the plateau’s properties are elucidated. The paper offers a totally new window for biomechanics, especially for biomimicking design of chatter vibration systems inspired by the agglomerated roes.

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A professional semi-analytical method to construct series solution to singular and nonsingular differential equations

Burqan,

El-Ajou

2025

Alexandria Engineering Journal

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The analysis for the dynamic pull-in of a micro-electromechanical system

Cited by 5 publications

References 26 publications

A modern analytic method to solve singular and non-singular linear and non-linear differential equations

A modern analytic method to solve singular and non-singular linear and non-linear differential equations

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

A professional semi-analytical method to construct series solution to singular and nonsingular differential equations

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