Nonlinear Vibration Solutions of Nano-Beams Considering Surface Effects
Bibliographic record
Abstract
Nonlinear free vibration of nanobeams considering the surface effects is studied. The governing differential equation of motion of the system employing the Euler-Bernoulli beam theory is derived. Galerkin method is utilized to obtain the nonlinear ordinary differential equation of nanobeams, which is a well-known type of the Duffing equation. The elliptical harmonic balance method, energy balance technique and the variational approach are employed to obtain the frequency-amplitude relationship of the system. The effects of different parameters, i.e., aspect ratio, nonlocal parameter and the resultant residual stress, on the natural frequency are examined. Moreover, the variation of the amplitude on the frequency response is studied. The influence of the initial amplitude on the obtained modulus from the elliptical harmonic balance has been examined. Furthermore, the exact numerical solution is determined to verify the results obtained from the analytical solutions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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 teacher head, 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".