Analytical Modeling and Experimental Verification of Nonlinear Mode Coupling in a Decoupled Tuning Fork Microresonator
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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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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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