A closed-form model for the pull-in voltage of electrostatically actuated cantilever beams
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Bibliographic record
Abstract
A simple computationally efficient closed-form model has been developed to determine the pull-in voltage of a cantilever beam actuated by electrostatic force. The approach is based on a linearized uniform approximate model of the nonlinear electrostatic pressure and the load deflection model of a cantilever beam under uniform pressure. The linearized electrostatic pressure includes the electrostatic pressure due to the fringing field capacitances and has been derived from Meijs and Fokkema's highly accurate empirical expression for the capacitance of a VLSI on-chip interconnect. The model has been verified by comparing the results with published experimentally verified 3D finite element analysis results and also with results from similar closed-form models. The new model can evaluate the pull-in voltage for a cantilever beam with a maximum deviation of ±2% from the finite element analysis results for wide beams, and a maximum deviation of ±1% for narrow beams (extreme fringing field).
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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)
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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