Reduced-order modeling of squeeze-film damped electrostatically actuated microbeams using complex modes of the coupled problem
Abstract
A reduced-order model is developed for the nonlinear dynamics of electrostatically actuated microbeams, including the full squeeze film effect. The model uses Petrov-Galerkin projection on damped complex modes of the fully coupled fluid-structure problem. The Euler-Bernoulli theory for calmped-clamped and clamped-free microbeams, with mid-plane stretching and electrostatic nonlinearities, and the nonlinear compressible Reynolds equation are discretized by the differential quadrature method for the static solution and eigenvalue problem. The calculated eigenmodes are either complex conjugates describing the coupled behavior of the device or real depicting the fluid relaxation. The natural frequencies and quality factors are compared to experimental and numerical results found in the literature. Depending on the ambient pressure, the geometry of the microbeam, and the fluid boundary conditions, squeeze-film effect can impact not only the effective damping of the device but also its dynamics. It is shown that in some cases dropping fluid relaxation modes cannot be compensated by any set of purely structural modes. The non-classical damping introduced by the fluid modes is a spatially distributed phase difference between pressure and deflection. The convergence analysis of the dynamic response resulting from the reduced-order model showed that a basis with one set of coupled modes and one fluid mode can reproduce the results of a fully discretized model within 1.5% error and at much faster computational time.
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BibTeX
@misc{najar2026reducedorder,
title = {{Reduced-order modeling of squeeze-film damped electrostatically actuated microbeams using complex modes of the coupled problem}},
author = {Fehmi Najar},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07205},
eprint = {2611.07205},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07205},
}
RIS
TY - UNPB
TI - Reduced-order modeling of squeeze-film damped electrostatically actuated microbeams using complex modes of the coupled problem
AU - Fehmi Najar
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07205
UR - https://arxiv.org/abs/2611.07205
AB - A reduced-order model is developed for the nonlinear dynamics of electrostatically actuated microbeams, including the full squeeze film effect. The model uses Petrov-Galerkin projection on damped complex modes of the fully coupled fluid-structure problem. The Euler-Bernoulli theory for calmped-clamped and clamped-free microbeams, with mid-plane stretching and electrostatic nonlinearities, and the nonlinear compressible Reynolds equation are discretized by the differential quadrature method for the static solution and eigenvalue problem. The calculated eigenmodes are either complex conjugates describing the coupled behavior of the device or real depicting the fluid relaxation. The natural frequencies and quality factors are compared to experimental and numerical results found in the literature. Depending on the ambient pressure, the geometry of the microbeam, and the fluid boundary conditions, squeeze-film effect can impact not only the effective damping of the device but also its dynamics. It is shown that in some cases dropping fluid relaxation modes cannot be compensated by any set of purely structural modes. The non-classical damping introduced by the fluid modes is a spatially distributed phase difference between pressure and deflection. The convergence analysis of the dynamic response resulting from the reduced-order model showed that a basis with one set of coupled modes and one fluid mode can reproduce the results of a fully discretized model within 1.5% error and at much faster computational time.
ER -