Dynamic Analysis of a Digital Micromirror Device
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Bibliographic record
Abstract
We developed a distributed-parameter model (partial differential equations and associated boundary conditions) that describe the coupled torsion and bending motions of the Digital Micromirror Device (DMD) using the extended Hamilton principle. The work done by the electrostatic field is expressed in the form of a potential energy. It is found that coupling between the torsion and bending motions appears in the boundary conditions. The nonlinearity is mainly due to the application of the electrostatic forces and moments. Nonlinear terms appear only in the boundary conditions. The developed model provides a basis for a thorough study of the static and dynamic behaviors of the electromechanical device. The static response of the DMD for different DC loads shows the occurrence of pull-in (snap-down) instability at critical voltage values corresponding to the collapse of the yoke to mechanical stops. Estimates of the voltage, angle, and deflection at pull-in are given. The dynamic behavior of the DMD is analyzed by plotting the natural frequencies versus the applied DC voltage. We conducted a study of the sensitivity of the static and dynamic behaviors of the micromirror to variations in the geometric parameters of the DMD. It is found that the thickness and width of the hinges are the key parameters influencing the occurrence of static pull-in and the values of the voltage, angle, and deflection at pull-in.
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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 | 0.001 |
| 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