Regularized model of post-touchdown configurations in electrostatic MEMS: Interface dynamics

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7 Citations (Scopus)

Abstract

Interface dynamics of post-contact states in regularized models of electrostatic-elastic interactions are analysed. A canonical setting for our investigations is the field of Micro-Electromechanical Systems (MEMS) in which flexible elastic structures may come into physical contact due to applied Coulomb forces. We study the dynamic features of a recently derived regularized model (Lindsay, A. E. et al. 2014 Regularized model of post-touchdown configurations in electrostatic MEMS: equilibrium analysis. Physica D), which describes the system beyond the quenching singularity associated with touchdown, that is after the components of the device have come together. We build on our previous investigations of steady-state solutions by describing how the system relaxes towards these equilibria. This is accomplished by deriving a reduced dynamical system that governs the evolution of the contact set, thereby providing a detailed description of the intermediary dynamics associated with this bistable system. The analysis yields important practical information on the timescales of equilibration.

Original languageEnglish (US)
Pages (from-to)1635-1663
Number of pages29
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume80
Issue number6
DOIs
StatePublished - 2015

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Interface Dynamics
Micro-electro-mechanical Systems
System Dynamics
Electrostatics
MEMS
Contact
Configuration
Equilibrium Analysis
Bistable System
Quenching
Steady-state Solution
Systems Analysis
Dynamical systems
Time Scales
Dynamical system
Model
Singularity
Interaction

Keywords

  • Interface dynamics
  • Mechanical bistability
  • Nano-technology
  • Singular perturbation techniques

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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title = "Regularized model of post-touchdown configurations in electrostatic MEMS: Interface dynamics",
abstract = "Interface dynamics of post-contact states in regularized models of electrostatic-elastic interactions are analysed. A canonical setting for our investigations is the field of Micro-Electromechanical Systems (MEMS) in which flexible elastic structures may come into physical contact due to applied Coulomb forces. We study the dynamic features of a recently derived regularized model (Lindsay, A. E. et al. 2014 Regularized model of post-touchdown configurations in electrostatic MEMS: equilibrium analysis. Physica D), which describes the system beyond the quenching singularity associated with touchdown, that is after the components of the device have come together. We build on our previous investigations of steady-state solutions by describing how the system relaxes towards these equilibria. This is accomplished by deriving a reduced dynamical system that governs the evolution of the contact set, thereby providing a detailed description of the intermediary dynamics associated with this bistable system. The analysis yields important practical information on the timescales of equilibration.",
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author = "Lindsay, {A. E.} and Lega, {Joceline C} and Glasner, {Karl B}",
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T2 - Interface dynamics

AU - Lindsay, A. E.

AU - Lega, Joceline C

AU - Glasner, Karl B

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N2 - Interface dynamics of post-contact states in regularized models of electrostatic-elastic interactions are analysed. A canonical setting for our investigations is the field of Micro-Electromechanical Systems (MEMS) in which flexible elastic structures may come into physical contact due to applied Coulomb forces. We study the dynamic features of a recently derived regularized model (Lindsay, A. E. et al. 2014 Regularized model of post-touchdown configurations in electrostatic MEMS: equilibrium analysis. Physica D), which describes the system beyond the quenching singularity associated with touchdown, that is after the components of the device have come together. We build on our previous investigations of steady-state solutions by describing how the system relaxes towards these equilibria. This is accomplished by deriving a reduced dynamical system that governs the evolution of the contact set, thereby providing a detailed description of the intermediary dynamics associated with this bistable system. The analysis yields important practical information on the timescales of equilibration.

AB - Interface dynamics of post-contact states in regularized models of electrostatic-elastic interactions are analysed. A canonical setting for our investigations is the field of Micro-Electromechanical Systems (MEMS) in which flexible elastic structures may come into physical contact due to applied Coulomb forces. We study the dynamic features of a recently derived regularized model (Lindsay, A. E. et al. 2014 Regularized model of post-touchdown configurations in electrostatic MEMS: equilibrium analysis. Physica D), which describes the system beyond the quenching singularity associated with touchdown, that is after the components of the device have come together. We build on our previous investigations of steady-state solutions by describing how the system relaxes towards these equilibria. This is accomplished by deriving a reduced dynamical system that governs the evolution of the contact set, thereby providing a detailed description of the intermediary dynamics associated with this bistable system. The analysis yields important practical information on the timescales of equilibration.

KW - Interface dynamics

KW - Mechanical bistability

KW - Nano-technology

KW - Singular perturbation techniques

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