Modelling and dynamic analysis of a MEMS ring resonator supported by circular curved shaped inner beams
Bibliographic record
Abstract
Abstract Microelectromechanical systems (MEMS) based ring shaped resonators usually have a ring supported by spoke shaped springs. In this paper, we developed a general analytical model that can determine the natural frequency of any MEMS ring resonator considering effective mass and stiffness of spokes in both radial and tangential displacements. Our model is also able to determine the stiffness of the circular curved beam with arbitrary central angle. The well-known energy based Castigliano’s method was used to calculate the stiffness of a circular curved beam considering both flexural and axial rigidities. The stiffness of a circular curved beam with different central angles was determined and compared with the literature and finite element method (FEM). The results show that for the case of a central angle of the curved beam larger than 60 degrees, the deviation between the FEM and analytical approach is less than 1%. The potential energy and kinetic energy of the outside ring and spokes were determined based on the displacement function. The natural frequency of a ring resonator with different number of circular curved beams in the form of petals in modes n = 2 and n = 3 were determined and the results were compared with a numerical approach using FEM. The deviations between the analytical approach and numerical method are less than 4%.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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".