Passive Regulation of Thermally Induced Axial Force and Displacement in Microbridge Structures
Bibliographic record
Abstract
The analytical model of a mechanism for regulating the thermally induced axial force and displacement in a fixed–fixed microbeam is presented in this article. The mechanism which consists of a set of parallel chevron beams replaces one of the fixed ends of the microbeam. The thermomechanical behavior of the system is modeled using Castigliano’s theorem. The effective coefficient of thermal expansion is used in the analytical model. The analytical model takes into account both the axial and bending deformations of the chevron beams. The model provides a closed-form equation to determine the thermally induced axial force and displacement in the microbeam. In addition, the model is used to derive the equations for the sensitivities of the microbeam’s axial force and displacement to the variations of the design parameters involved. Moreover, the model produces the stiffness of the chevron beams. The effect of the stiffness of the chevron beams on the dynamic behavior of the microbeam is discussed. The analytical model is verified by finite element modeling using a commercially available software package. Using the analytical model, two special cases are highlighted: a system with thermally insensitive axial force and a system with thermally insensitive axial displacement. The main application of the model presented in this article is in the design of sensors and resonators that require robustness against changes of temperature in the environment. The analytical model and the sensitivity equations can be easily integrated into optimization algorithms.
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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 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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".