Theory of Thermoelastic Damping in Micromechanical Resonators With Two-Dimensional Heat Conduction
Bibliographic record
Abstract
Analysis of thermoelastic damping (TED) is an important component of the design of low-loss vacuum-operated micro- and nanomechanical resonators used in microelectro- mechanical systems (MEMS). The quasi-1-D theories developed by Zener in 1937, and subsequently improved by Lifshitz and Roukes in 2000, are now widely used in MEMS design. This paper presents an exact theory for TED with 2-D heat conduction that enables a detailed evaluation of the accuracy of the quasi-1-D theories. A Green's function method is used to solve the 2-D heat- conduction equation, and an expression for TED is derived in the form of an infinite series. The effects of beam geometry, length-to- thickness aspect ratio, natural frequency, flexural mode shapes, and structural boundary conditions on TED are investigated for the representative case of single-crystal silicon microbeam resonators. The errors in the exact quasi-1-D theory range from 2% to 80% depending upon the aspect ratio and the mode shape. Implications for the use of the quasi-1-D and 2-D theories in MEMS design are discussed. [2007-0199].
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 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".