Addressing the needs of complex MEMS design

Clark, Jason K.; Bindel, David; Kao, W. F.; Zhu, Edward L.; Kuo, Arthur D.; Zhou, Ningning; Nie, Jiahong; Demmel, James; Bai, Zhaojun; Govindjee, Sanjay; Pister, Kristofer S. J.; Gu, M.; Agogino, Alice M.

doi:10.1109/memsys.2002.984240

Cited by 28 publications

(19 citation statements)

References 3 publications

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“…For a given voltage v, we substitute the static solution corresponding to the lower branch into the Jacobian matrix of Equation (11) and find the corresponding eigenvalues. Then by taking the square root of the magnitudes of the individual eigenvalues, we obtain the natural frequencies of the device.…”

Section: Microbeamsmentioning

confidence: 99%

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Reduced-Order Models for MEMS Applications

2005

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We review the development of reduced-order models for MEMS devices. Based on their implementation procedures, we classify these reduced-order models into two broad categories: node and domain methods. Node methods use lower-order approximations of the system matrices found by evaluating the system equations at each node in the discretization mesh. Domainbased methods rely on modal analysis and the Galerkin method to rewrite the system equations in terms of domain-wide modes (eigenfunctions). We summarize the major contributions in the field and discuss the advantages and disadvantages of each implementation. We then present reduced-order models for microbeams and rectangular and circular microplates. Finally, we present reduced-order approaches to model squeeze-film and thermoelastic damping in MEMS and present analytical expressions for the damping coefficients. We validate these models by comparing their results with available theoretical and experimental results. State-of-the-ArtThe dynamics of MEMS are represented by partial-differential equations (PDEs) and associated boundary conditions. The most widely used method to treat these distributed-parameter problems is to reduce them to ordinary-differential equations (ODEs) in time and then solve the reduced equations either numerically or analytically. Three approaches are used in the reduction.• Idealization of the device flexible structural elements as rigid bodies.• Discretization using finite-element methods (FEM), boundary-element methods (BEM), or finitedifference methods (FDM). • Construction of reduced-order models (ROM).The first and second approaches, while lying at opposite extremes of complexity, are currently the most widely used. The pressure for better designs, less trial-and-error in the design process, and better device performance demands better models than idealized rigid bodies. Numerous researchers compared the pull-in voltage of electrostatically actuated cantilever [1] and clamped-clamped [2] microbeams obtained by solving the distributed-parameter system to those obtained using a spring-mass model and found that the spring-mass model underpredicts the pull-in voltage.Although FEM/BEM and FDM simulations are adequate for the analysis of the static deflections (equilibrium positions) of MEMS devices, they are inadequate for dynamic simulations because they require the time integration of thousands of second-order ODEs (one for each degree of freedom in the model). This is a very expensive process, making system-level simulation, device optimization, interactive design, and evolutionary design almost impossible. As a result, reduced-order modeling of MEMS is gaining attention as a way to balance the need for enough fidelity in the model against the numerical efficiency necessary to make the model of practical use in MEMS design.

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Section: Microbeamsmentioning

confidence: 99%

“…We plug the φ i and ω i corresponding to the first M symmetric modes into Equation (11) and integrate them in time for the u i (t). To obtain the deflection variation with time, we use Equation (10) with the calculated φ i and u i (t).…”

Section: Microbeamsmentioning

confidence: 99%

Reduced-Order Models for MEMS Applications

2005

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“…This study describes finite element analysis (FEA) modeling tools used in the design phase of optical MEMS. Current modeling tools are useful for design verification, but are not often used in the early phases of design [40], although, this work shows that FEA modeling can be used as a predictive design tool. This section will first cover analytical modeling methods for simple structures.…”

Section: Modeling and Simulation Of Mirror Figurementioning

confidence: 97%

Ultra-lightweight telescope with MEMS adaptive optic for distortion correction.

Spahn¹,

Cowan²,

Shaw³

et al. 2004

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DO NOT DESTROY RETURN TO LIBRARY VAULTABSTRACT Recent world events have underscored the need for a satellite based persistent global surveillance capability. To be useful, the satellite must be able to continuously monitor objects the size of a person anywhere on the globe and do so at a low cost.One way to satisfy these requirements involves a constellation of satellites in low earth orbit capable of resolving a spot on the order of 20 cm. To reduce cost of deployment, such a system must be dramatically lighter than a traditional satellite surveillance system with a high spatial resolution. The key to meeting this requirement is a lightweight optics system with a deformable primary and secondary mirrors and an adaptive optic subsystem correction of wavefront distortion. This proposal is concerned with development of MEMS micromirrors for correction of aberrations in the primary mirror and improvement of image quality, thus reducing the optical requirements on the deployable mirrors. To meet this challenge, MEMS micromirrors must meet stringent criteria on their performance in terms of flatness, roughness and resolution of position. Using Sandia's SUMMIT foundry which provides the world's most sophisticated surface MEMS technology as well as novel designs optimized by finite element analysis will meet severe requirements on mirror travel range and accuracy.

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“…Example 3 This example is from the frequency response simulation of a torsional micromirror described in [37]. By using a lumped finite element analysis, it results in a second Applying the SOAR-based method to the system, we find that a reduced second system of order n = 20 is sufficient for the desired accuracy.…”

Section: H( S ) =/T((s-so)~m + ( S -So)i) + K)-lbmentioning

confidence: 99%

Second-order Krylov subspace and arnoldi procedure

Bai

2004

J. of Shanghai Univ.

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We report our recent work on a second-order Krylov subspace and the corresponding second-order Arnoldi procedure for generating its orthonurmal basis. The second-order Krylov subspace is spanned by a sequence of vectors defined vm a second-order linear homogeneous recurrence relation with coefficient matrices A and B and an initial vector u. It generalizes the well-known Krylov subspace ~,(A ; v), which is spanned by a sequence of vectors defined via a first-order linear homogeneous recurrence relation with a single coefficient matrix A and an initial vector v. The applications are shown for the solution of quadratic eigenvalue problems and dimension reduction of second-order dynamical systems. The new approaches preserve essential structures and properties of the quadratic eigenvalue problem and second-order system, and demonstrate superior numerical results over the common approaches based on linearization of these second-order problems.

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Addressing the needs of complex MEMS design

Cited by 28 publications

References 3 publications

Reduced-Order Models for MEMS Applications

Reduced-Order Models for MEMS Applications

Ultra-lightweight telescope with MEMS adaptive optic for distortion correction.

Second-order Krylov subspace and arnoldi procedure

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