Analytical Modeling and Experimental Verification of Nonlinear Mode Coupling in a Decoupled Tuning Fork Microresonator
Bibliographic record
Abstract
This paper provides the analytical and experimental studies into the nonlinear mode coupling in a tuning fork microresonator, with electrostatic actuation at forced and internal resonance frequencies. The analytical investigation leads to modal equations that take into account kinematic and electrostatic nonlinearities. The equations of motion are derived using Lagrange's energy method. The theoretical resonance curves are determined by using the two-variable expansion perturbation technique near simultaneous subharmonic and internal resonances. The two desired mode shapes of the device are tailored to establish an approximate two-to-one frequency ratio between their natural frequencies. A sample device design is fabricated in a commercial foundry process. The influence of AC driving levels and a detuning parameter, due to inevitable fabrication imperfections, on the system dynamics are investigated theoretically and experimentally. It is shown that the deviation from ideal internal resonance condition separates the region of the nonlinear vibration into two distinct excitation frequencies. The model and simulated results obtained by the perturbation analysis are validated by comparing them with the experimental results.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".