Nonlinear Analysis of MEMS Electrostatic Microactuators: Primary and Secondary Resonances of the First Mode*
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Bibliographic record
Abstract
We use a discretization technique that combines the differential quadrature method (DQM) and the finite difference method (FDM) for the space and time, respectively, to study the dynamic behavior of a microbeam-based electrostatic microactuator. The adopted mathematical model based on the Euler— Bernoulli beam theory accounts for the system nonlinearities due to mid-plane stretching and electrostatic force. The nonlinear algebraic system obtained by the DQM—FDM is used to investigate the limit-cycle solutions of the microactuator. The stability of these solutions is ascertained using Floquet theory and/or long-time integration. The method is applied for large excitation amplitudes and large quality factors for primary and secondary resonances of the first mode in case of hardening-type and softening-type behaviors. We show that the combined DQM—FDM technique improves convergence of the dynamic solutions. We identify primary, subharmonic, and superharmonic resonances of the microactuator. We observe the occurrence of dynamic pull-in due to subharmonic and superharmonic resonances as the excitation amplitude is increased. Simultaneous resonances of the first and higher modes are identified for large orbits in both primary and secondary resonances.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it