Lyapunov exponents as a criterion for the dynamic pull-in instability of electrostatically actuated microstructures

Slava Krylov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The dynamic pull-in instability of double clamped microscale beams actuated by a suddenly applied distributed electrostatic force and subjected to non-linear squeeze film damping is investigated. A reduced order model is built using the Galerkin decomposition with undamped linear modes as base functions and verified through comparison with numerical finite differences solution. The stability analysis of a beam actuated by one and two electrodes symmetrically located at two sides of the beam and operated by a step-input voltage is performed by evaluating the largest Lyapunov exponent, the sign of which defines the character of the response. It is shown that this approach provides an efficient quantitative criterion for the evaluation of dynamic pull-in instability, especially when combined with compact reduced order models. Based on the Lyapunov exponent criterion, the influence of various parameters on the beam dynamic stability is investigated.

Original languageEnglish
Pages (from-to)626-642
Number of pages17
JournalInternational Journal of Non-Linear Mechanics
Volume42
Issue number4
DOIs
StatePublished - May 2007

Keywords

  • Dynamic pull-in
  • Electrostatic actuator
  • Lyapunov exponents
  • Reduced order model

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