Dynamics and Control of Electrostatic Structures

Silverberg, Larry; Weaver, L.

doi:10.1115/1.2788876

Cited by 6 publications

(3 citation statements)

References 3 publications

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“…(10) In (10), w (m,i) , l (m,i) , and S (m,i) denote the width, length, and area of the electrode region for a point charge q (m,j ) , respectively (see the illustration in the right hand top corner of Fig. 1).…”

Section: Formulations Based On Point Chargesmentioning

confidence: 99%

“…Therefore, the voltage V (m,j ) at the location of each point charge, q (m,i) , should be accounted for in the formulation. If there are 2N tot electrodes, the total electrostatic energy induced by the point charges can then be calculated as follows [10,11]:…”

Section: Formulations Based On Point Chargesmentioning

confidence: 99%

“…It is reported that the charge points at distinct locations on the electrode of a structure can be used to calculate the electrostatic interactions between electrodes [10,11]. If the point charges are defined on the lumped masses, the equations of motion can be easily obtained by expressing the electrostatic forces in terms of their positions and charge values.…”

Section: Introductionmentioning

confidence: 99%

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A multibody-based dynamic simulation method for electrostatic actuators

et al. 2007

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A numerical simulation method is developed to analyze the dynamic responses of electrostatic actuators, which are electromechanically-coupled systems. The developed method can be used to determine the dynamic responses of cantilever-type switches, which are an example of typical MEMS (Micro-Electro-Mechanical System) devices driven by an electrostatic force. We propose the approach that adopts a point charge to deal with electric field effects between electrodes. This approach may be considered as a lumped parameter model for the electrostatic interactions. An advantage of this model may be the easy incorporation of the electrostatic effects between electrodes into a multibody dynamics analysis algorithm. The resulting equations contain the variables for position, velocity, and electric charge to describe the motion of the masses and the charges on the electrodes in a system. By solving these equations simultaneously, the dynamic response of an electrostatically-driven system can be correctly simulated. In order to realize this approach, we implement the procedures into RecurDyn, the multibody dynamics software developed by the authors. The developed numerical simulation tool was evaluated by applying it to cantilever-type electrostatic switches in many different driving conditions. The results suggest that the developed tool may be useful for predicting behaviors of electrostatic actuators in testing as well as in design.

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Section: Formulations Based On Point Chargesmentioning

confidence: 99%

Section: Formulations Based On Point Chargesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A multibody-based dynamic simulation method for electrostatic actuators

et al. 2007

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Dynamic modeling of interactions between fields and matter in MEMS devices

Zeng¹,

Liu²,

Korvink³

2004

Microsystem Technologies

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Dynamic modeling of interactions between fields and matter in MEMS devices

Zeng

Liu

Korvink

2004

Microsystem Technologies

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In this work, we propose an innovative and general mathematical modeling framework with Lagrangian functions of multi-coupled energy domains for MEMS devices in the material frame. Due to the advantage of material descriptions of continua and the uniformity of Lagrangians for different physical domains, this framework simplifies the numerical analyses of MEMS devices. IntroductionA complete physical model for a MEMS device could lead us into all areas of continuum physics [1][2][3][4][5][6][7][8]. In the present work, we limit ourselves to the mechanical and electromagnetic energy domains. The physical model for a MEMS device is consequently regarded as consisting of two submodels. The first one is a dynamic mechanical submodel describing the mechanics of the elastic deformation structure. The second one is an electromagnetic submodel describing the dynamics of the electromagnetic influence within a MEMS device. These two submodels are mutually coupled.Following the Lagrangian dynamics approach [9-17], we present a new framework for modeling a MEMS device based on the theories of continuum mechanics [18][19][20] and electrodynamics [21][22][23][24][25][26]. In this framework, the deformation field and electromagnetic field are rendered down to unified and consistent representation forms. By the transformations from spatial forms into material forms, fully coupled dynamic equations are rigorously derived. This framework is comprehensive and extensible. It can be extended further to track other energy domains and generate a complete physical model for multi-physical domain MEMS devices. This formalism is not only powerful for theoretical reasoning but also for numerical processing. Because of the uniformity of the approach for different physical domains, a general discretization framework can be set up. Lagrange formalismThe Lagrange formalism determines the model for a dynamic system, the equations of motion, through a variation principle applied to the proposed Lagrangian which stands de facto for the energy functions of the system. This approach exploits the use of so-called generalized coordinates, i.e., any set of variables sufficient in number to locate unambiguously the configuration of the dynamic system. Generalized coordinates are not alternatives to reference coordinate systems, but are descriptions of the kinematic configuration of the dynamic system based on the system degrees of freedom.For the continuum model, which has an infinite number of degrees of freedom, the generalized coordinates constitute fields. By defining the Lagrangian in terms of these fields as a functional of the fields, the Lagrange formalism allows the variational principle to be employed in a variety of physical energy domains.In the Lagrangian formulation, the Lagrangian L of a continuous system in the Euclidean space R 3 is a volume integral over the system domain D:where r z is the gradient operator at z 2 R 3 and the Lagrangian density Lðn; _ n; r z n; z; tÞ depends on the ordered array of fields n 2 R n , its generalized vel...

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Dynamics and Control of Electrostatic Structures

Cited by 6 publications

References 3 publications

A multibody-based dynamic simulation method for electrostatic actuators

A multibody-based dynamic simulation method for electrostatic actuators

Dynamic modeling of interactions between fields and matter in MEMS devices

Dynamic modeling of interactions between fields and matter in MEMS devices

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