Continuum Models Incorporating Surface Energy for Static and Dynamic Response of Nanoscale Beams
Bibliographic record
Abstract
Nanoscale beams are commonly found in nanomechanical and nanoelectromechanical systems (NEMS) and other nanotechnology-based devices. Surface energy has a significant effect on nanoscale structures and is associated with their size-dependent behavior. In this paper, a general mechanistic model based on the Gurtin-Murdoch continuum theory accounting for surface energy effects is presented to analyze thick and thin nanoscale beams with an arbitrary cross section. The main contributions of this paper are a set of closed-form analytical solutions for the static response of thin and thick beams under different loading (point and uniformly distributed) and boundary conditions (simply-supported, cantilevered, and clamped ends), as well as the solution of the free vibration characteristics of such beams. Selected numerical results are presented for aluminum and silicon beams to demonstrate their salient response features. It is shown that classical beam theory is not accurate in situations where the surface residual stress and/or surface elastic constants are relatively large. An intrinsic length scale for beams is identified that depends on beam surface properties and cross-sectional shape. The present work provides a convenient set of analytical tools for researchers working on NEMS design and fabrication to understand the static and dynamic behavior of nanoscale beams including their size-dependent behavior and the effects of common boundary conditions.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".