Multipole BEM for the evaluation of damping forces on MEMS

Frangi, Attilio; Gioia, Antonio Di

doi:10.1007/s00466-005-0694-1

Cited by 46 publications

(27 citation statements)

References 9 publications

(14 reference statements)

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“…Reliable tools exist for the prediction of gas damping in the first two regimes (see e.g. [4,5,8,5,9]) but the situation is less defined at lower pressures. Even though numerical techniques of deterministic and statistical nature have been developed in the transition regime, their application to realistic 3D low-speed MEMS is still under investigation.…”

Section: Introductionmentioning

confidence: 99%

Analysis of fluid‐structure interaction in low pressure MEMS by Integral Equations

Frangi

2008

Proc Appl Math and Mech

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The evaluation of gas dissipation occurring in inertial polysilicon MEMS is addressed focusing the attention on the freemolecule flow. In this regime, which is very often of interest for industrial applications, collisions between molecules can be neglected and the momentum transfer to the moving shuttle can be easily computed. Since the surfaces of silicon MEMS are generally very rough, a complete diffusion model is adopted to describe the wall-molecule interaction. A Boundary Integral Equation approach is proposed and it is shown that the introduction of the key assumption of small perturbations is crucial in the development of a robust and fast numerical tool.

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Section: Introductionmentioning

confidence: 99%

Analysis of fluid‐structure interaction in low pressure MEMS by Integral Equations

Frangi

2008

Proc Appl Math and Mech

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“…Having shown in section 3.1 that selecting L according to (18) does not guarantee that G L given by (14) approximates G sufficiently well in the complex-wavenumber case, a modified selection rule that depends on the damping level β, where…”

Section: New Damping-dependent Selection Rule For Truncation Parameter Lmentioning

confidence: 99%

“…The size of the problem is N = 307, 224, and the octree for each region has a leaf levell 1 =l 2 = 5. This problem has been solved with L set using either the elastic rule (18) or the damping-dependent rule (24). Results on the relative error between the numerical and analytical solutions for the displacement on the cavity wall and the interface between Ω 1 and Ω 2 are shown in Fig.…”

Section: Verification On a Two-region Examplementioning

confidence: 99%

“…The capabilities of the Fast Multipole-Boundary Element Method (FMBEM) and its recursive variant the Multi Level-FMBEM (ML-FMBEM) have rapidly progressed during the last decade, allowing many engineering applications requiring large BEM models, in connection with e.g. acoustics [16], elastodynamics [17], Stokes flows [18] or electromagnetism [19]. Fast BEMs have also been proposed using other approaches, in particular based on hierarchical matrices [20][21][22].…”

Section: Introductionmentioning

confidence: 99%

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Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics

Grasso

Chaillat

Bonnet

et al. 2012

Engineering Analysis with Boundary Elements

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. Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics. Engineering Analysis with Boundary Elements, Elsevier, 2012Elsevier, , 36, pp.744-758. <10.1016Elsevier, /j.enganabound.2011 Abstract This article extends previous work by the authors on the single-and multi-domain time-harmonic elastodynamic multi-level fast multipole BEM formulations to the case of weakly dissipative viscoelastic media. The underlying boundary integral equation and fast multipole formulations are formally identical to that of elastodynamics, except that the wavenumbers are complex-valued due to attenuation. Attention is focused on evaluating the multipole decomposition of the viscoelastodynamic fundamental solution. A damping-dependent modification of the selection rule for the multipole truncation parameter, required by the presence of complex wavenumbers, is proposed. It is empirically adjusted so as to maintain a constant accuracy over the damping range of interest in the approximation of the fundamental solution, and validated on numerical tests focusing on the evaluation of the latter. The proposed modification is then assessed on 3D single-region and multi-region viscoelastodynamic examples for which exact solutions are known. Finally, the multi-region formulation is applied to the problem of a wave propagating in a semi-infinite medium with a lossy semi-spherical inclusion (seismic wave in alluvial basin). These examples involve problem sizes of up to about 3 10 5 boundary unknowns.

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“…In order to cure this issue, a new BEM, the mixed velocity traction approach, has been recently proposed in reference and further developed for large-scale problems in Frangi and Di Gioia. 36 A change in the fundamental frequency would result and this change would be dependent on the mass variation. These sensors can thus be called mass sensors.…”

Section: Introductionmentioning

confidence: 99%

The oscillating and electrostatic characteristics of microelectromechanical system cantilever structure analyzed based on the air gap domain

Jian

Zhang

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

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Extensive modeling and simulation of the damping phenomenon, electrostatic actuation, and structural vibration analysis are performed. The governing partial differential equations of cantilever plate are obtained, and the resonant frequencies are calculated from the equilibrium equations. The damping forces of squeeze film are analyzed by obtaining the damping ratio and spring constant. Electrostatic actuation is applied to oscillate the cantilever to ensure that the displacement of the plate is above the thermal noise floor. Electrostatic actuating forces, displacement, and capacitance are calculated both numerically and analytically from the Poisson's equations. Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. Squeeze film effects are simulated by the finite element method. The accuracy of the compact model is studied by comparing its response to the numerical results calculated with the finite element method. The agreement is very good in a wide frequency band. The numerical study and the compact model are directly applicable in predicting the damping force and damping factors of squeeze film.

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Multipole BEM for the evaluation of damping forces on MEMS

Cited by 46 publications

References 9 publications

Analysis of fluid‐structure interaction in low pressure MEMS by Integral Equations

Analysis of fluid‐structure interaction in low pressure MEMS by Integral Equations

Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics

The oscillating and electrostatic characteristics of microelectromechanical system cantilever structure analyzed based on the air gap domain

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