Some design considerations on the electrostatically actuated microstructures

Hu, Yu; Chang, Che‐Chen; Huang, Shan-You

doi:10.1016/j.sna.2003.12.012

Cited by 173 publications

(139 citation statements)

References 16 publications

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“…The relative errors of results obtained from ALM are comparable to those in [17] and [16], for all cases of finite element approximations. In fact, it appears …”

Section: Numerical Testssupporting

confidence: 53%

“…Hu, Chang and Huang [17] first studied such a problem in 2004. The structure [17] can be schematically described as a thin metal beam hanging over a substrate separated by some insulator, where one end of the microbeam is fixed and the other is free (fixed-free beam). The beam is pulled (deflected) towards the substrate when a voltage is applied between the beam and the substrate.…”

Section: Numerical Testsmentioning

confidence: 99%

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Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential Equations

Li¹

2017

JAMP

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A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions to engineering problems. These engineering problems are described by differential equations with boundary values and are formulated as optimization of some functionals. The algorithm achieves its simplicity and versatility by choosing linear equality relations recursively for the augmented Lagrangian associated with an optimization problem. We demonstrate the formulation of an optimization functional for a 4th order nonlinear differential equation with boundary values. We also derive the associated augmented Lagrangian for this 4th order differential equation. Numerical test results are included that match up with well-established experimental outcomes. These numerical results indicate that the new algorithm is fully capable of producing accurate and stable solutions to differential equations.

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“…The relative errors of results obtained from ALM are comparable to those in [17] and [16], for all cases of finite element approximations. In fact, it appears …”

Section: Numerical Testssupporting

confidence: 53%

Section: Numerical Testsmentioning

confidence: 99%

Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential Equations

Li¹

2017

JAMP

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show abstract

“…Determination of the pull-in voltage is critical in the design of MEMS devices. Accurate determination of pull-in voltage is very challenging in virtue of the electromechanical coupling effect and the nonlinearity of electrostatic force [3,4]. Effects such as the fringing field and the initial residual stress further complicate the modeling.…”

Section: Introductionmentioning

confidence: 99%

Closed form solutions for the pull-in voltage of micro curled beams subjected to electrostatic loads

2006

J. Micromech. Microeng.

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This paper derives a closed form solution with fringing filed effects for the pull-in voltages of the micro fixed-fixed beam subjected to electrostatic loads and initial stress. The closed form solution is derived based on the Euler's beam theory and the energy method. The accuracy of the present closed form solution is verified through comparing with the experimentally measured data of the published literatures. The error of the present closed form solution is within 1% compared to the measured data. The present closed form solution is more accurate than the past works and is very simple and highly accurate for implementation in the design of MEMS.

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“…Lump model estimates the pull-in limit as one-third of the initial gap (d/3). However, experimental part of a study showed that pull-in limit is at a different value (Hu et al, 2004). Hu et al utilized a linearized governing equation of a cantilever to demonstrate their analytical approach.…”

Section: Introductionmentioning

confidence: 99%

New Approach to Pull-In Limit and Position Control of Electrostatic Cantilever Within the Pull-in Limit

Yıldız¹,

Ak²,

Canbolat³

2012

Electrostatics

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Some design considerations on the electrostatically actuated microstructures

Cited by 173 publications

References 16 publications

Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential Equations

Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential Equations

Closed form solutions for the pull-in voltage of micro curled beams subjected to electrostatic loads

New Approach to Pull-In Limit and Position Control of Electrostatic Cantilever Within the Pull-in Limit

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