Proper orthogonal decomposition and component mode synthesis in macromodel generation for the dynamic simulation of a complex MEMS device

Lin, W. Z.; Lee, K H; Lim, Siak Piang; Liang, Yanchun

doi:10.1088/0960-1317/13/5/316

Cited by 20 publications

(15 citation statements)

References 12 publications

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“…Lin et al [27] produced the first model of a complex device made of more than one primitive structural element (beam, plate, or desk). They used finite differences to generate a time series for a micro-mirror made of a plate suspended from two beams over an air gap and actuated by a step voltage beyond the pull-in voltage.…”

Section: Basis Set From Time Seriesmentioning

confidence: 99%

“…Osterberg developed a statistics-based model to approximate v pi and solved for the optimal statistical coefficients by fitting his model to the experimental data. Vogl and Nayfeh [48] fit the physics-based model, Equations (27) and (28), to the experimental data by solving for the values of E, σ, ν, d, and h that minimize the objective function (29) where the δ i , v model …”

Section: Reduced-order Models For Mems Applicationsmentioning

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: Basis Set From Time Seriesmentioning

confidence: 99%

Section: Reduced-order Models For Mems Applicationsmentioning

confidence: 99%

Reduced-Order Models for MEMS Applications

2005

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show abstract

“…Then the proper orthogonal decomposition method (Singular Value Decomposition -SVD , Karhunen -Loève decomposition -KL and neural networks-based generalized Hebbian algorithm -GHA) is applied to the time series for extracting the mode shapes of the device structural elements. The choice of orthogonal basis functions φ k can be done by the following way [8]. First the MEMS dynamics are simulated using a slow but accurate technique such as FEM or FDM.…”

Section: Modal Rom Based On Proper Orthogonal Decomposition Methodsmentioning

confidence: 99%

“…By defining (4) second equations (2) can be transfer to the first (1). The FULL file contains all the information about the system: the system element matrices, Dirichlet boundary conditions, equation constrain and the load vector.…”

Section: Fem/fdm Modelmentioning

confidence: 99%