Variational Iteration Method for Prediction of the Pull-In Instability Condition of Micro/Nanoelectromechanical Systems

Anjum, Naveed; He, Ji‐Huan; He, Chun-Hui; Gepreel, Khaled A.

doi:10.1134/s1029959923030013

Cited by 9 publications

(2 citation statements)

References 46 publications

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“…The variational iteration method offers an unprecedented tool to dynamical analysis of the MEMS systems. 12–16…”

Section: Introductionmentioning

confidence: 99%

“…The variational iteration method offers an unprecedented tool to dynamical analysis of the MEMS systems. [12][13][14][15][16] Some symmetry-breaking behaviors hide the pull-in instability, while others may have the pull-down instability. The pull-down instability is a newly found dynamic motion for even nonlinear oscillators, which is proposed by professor He and his students.…”

Section: Introductionmentioning

confidence: 99%

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Symmetry-breaking and pull-down motion for the Helmholtz–Duffing oscillator

Niu,

He,

Alsolami

2023

Journal of Low Frequency Noise, Vibration and Active Control

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An accurate frequency of the Helmholtz–Duffing oscillator is obtained by a sophisticated modification of He’s frequency formulation. The pull-down instability existing in the symmetric breaking phenomenon is a newly discovered dynamic motion for oscillators with even nonlinearities. A criterion for predicting the asymmetrical amplitude motion and the pull-down instability is built by measuring the amplitude change. The good matching performance between the analytic results and numerical ones indicates that the criterion offers a starting point for future research into the pull-down phenomenon, and opens a new path for studying more complex nonlinear oscillators with even nonlinearities.

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“…The variational iteration method offers an unprecedented tool to dynamical analysis of the MEMS systems. 12–16…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetry-breaking and pull-down motion for the Helmholtz–Duffing oscillator

Niu,

He,

Alsolami

2023

Journal of Low Frequency Noise, Vibration and Active Control

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From periodic to pseudo-periodic motion and pull-in instability of the MWCNT actuator in the vicinity of the graphite sheets

Mohammadian

2024

Chinese Journal of Physics

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A highly accurate analytical method for determination of the vibrational frequency of N/MEMS with electrostatic and van der Waals interaction forces

Nhu Hieu,

Chung

2024

J. Micromech. Microeng.

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In this study, a novel approach based on the elliptic balance method is proposed for the first time to find the approximate frequency of nano/micro-electro-mechanical systems (N/MEMSs) modeled as the Euler-Bernoulli beams under the effect of electrostatic and van der Waals interaction forces. Firstly, the governing equation of the beam is reduced to the single-mode vibration equation using the Galerkin method. A nonlinear differential equation for the time dependent beam deflection is obtained. The authors have presented-the approximate solution as an elliptic cosine function, which considers the free term contributing to the solution. This free term is relevant for vibrations having a non-zero mean in time in which the beam is affected by a relatively large, applied voltage. By some manipulations, the obtained result is an algebraic equation with only one unknown in three unknowns: the free, vibration coefficient terms and modulus quantity of the elliptic cosine function. This nonlinear equation is solved using the Newton - Raphson method. Numerical results from the elliptic balance method show that the accuracy of the solution responses in time and approximate frequency is relatively accurate, almost coinciding with the results obtained from the numerical solution method using the Runge - Kutta algorithm. Our result also agrees well with previously published experimental and simulation results. The result is meaningful when determining the frequency of the vibrating beam with high accuracy for micro/nano systems.

show abstract

Variational Iteration Method for Prediction of the Pull-In Instability Condition of Micro/Nanoelectromechanical Systems

Cited by 9 publications

References 46 publications

Symmetry-breaking and pull-down motion for the Helmholtz–Duffing oscillator

Symmetry-breaking and pull-down motion for the Helmholtz–Duffing oscillator

From periodic to pseudo-periodic motion and pull-in instability of the MWCNT actuator in the vicinity of the graphite sheets

A highly accurate analytical method for determination of the vibrational frequency of N/MEMS with electrostatic and van der Waals interaction forces

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