Thermoelastic Damping in Layered Microresonators: Critical Frequencies, Peak Values, and Rule of Mixture
Bibliographic record
Abstract
The design of high-Qmicroresonators requires a careful evaluation of thermoelastic damping (TED). Here, we consider the widely used class of flexural-mode bilayered beam resonators consisting of a substrate coated with a thin film and derive an analytical expression in the form of an infinite series to compute the frequency dependence of TED. The nature and structure of the thermoelastic dissipation spectrum were explored by computing TED over several decades of frequency in a large set of materials and structures. TED exhibits a rich variety of spectral features that include multiple well-resolved peaks. An approximate rule of mixture was obtained by retaining only the leading term of the infinite series. The accuracy and utility of the one-term approximation, which can be regarded as the analog of Zener's formula for bilayered beams, are discussed. Taken together, our results can be used to optimize the design of layered microresonators and gain useful insight into a fundamental mechanism of dissipation.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".