Structural instability of a parallel array of mutually attracting identical microbeams
Bibliographic record
Abstract
A novel method is developed to study the structural instability of a parallel array of identical microbeams each of which interacts with two neighboring microbeams through distance-dependent surface attractive forces (such as electrostatic, van der Waals or Casimir forces). First, based on a simplified spring model, it is verified that the equilibrium deflections of intermediate beams (except the beams at the two ends of the parallel array) would be negligibly small. Thus, when the end-effect of the beams at the ends of the parallel array is neglected, exact analysis of parallel beams shows that the critical value of the beam–beam interaction coefficient for instability of the parallel array, defined on the initial distance between adjacent beams, is exactly a half of the critical value of the interaction coefficient for instability of two mutually attracting beams, or equivalently a quarter of the critical value of the interaction coefficient for instability of a single beam attracted by a rigid body. Furthermore, the end-effect is studied by examining the dependence of the critical value on the amplified interaction coefficient for the two end beams due to their non-negligible deflection caused by one-side attraction from the adjacent beam. The results show that the end-effect leads to a 20%–35% reduction of the critical interaction coefficient for instability of the parallel array, and therefore the actual critical value can be given, conservatively, by 60% of the critical value without the end-effect. These results provide a simple design criterion for the pull-in instability of interacting parallel microbeams. In particular, the results obtained by the present method are found to be in good agreement with known results for a few special cases and the exact data obtained by an iteration numerical method for the spring model.
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 | 0.000 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".