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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v6.i6.50
pages 563-584

Parametric Excitation and Stabilization of Electrostatically Actuated Microstructures

Slava Krylov
School of Mechanical Engineering, Tel Aviv University, Israel


The parametric instability of double-clamped microscale beams actuated by a time-varying distributed electrostatic force provided by two electrodes symmetrically located at two sides of the beam and subjected to nonlinear squeeze film damping is investigated. A reduced-order model is built using the Galerkin decomposition with undamped linear modes as base functions. The stability analysis is performed by evaluating the sign of the largest Lyapunov exponent, which defines the character of the response. It is shown that this approach provides an efficient quantitative criterion for the evaluation of parametric 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. We show that application of a time-dependent (ac) voltage in addition to a steady (dc) voltage exceeding the static stability limit may have a stabilizing influence while the structure, in accordance with the Lyapunov exponent criterion, remains stable. Parametric stabilization considered in this work represents an example of the strong influence of the fast-scale excitation on the slow-scale behavior.


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