Application of Variational Iteration Method in Nonlinear Free Vibration Analysis of Multi-Layered Nano-Scale Graphene Sheets
Bibliographic record
Abstract
The nonlinear free vibration of multi-layered nano-scale graphene sheets is studied. Using the von Kármán and nonlocal continuum theories, large amplitude of vibration is included in the analysis as well as the size effect of nano-structure. The SSSS boundary condition is considered for the multi-layered graphene sheet and coupled nonlinear differential equations of motion of layers are taken into account based on Galerkin method. Variational iteration method (VIM) is employed as the solution procedure and nonlinear natural frequencies of the system are analytically determined. Two different geometries are taken into account and the analytical results are compared with frequencies obtained by numerical method. Finally, influence of geometrical parameters and amplitude of vibration on nonlinear frequencies of the system is examined.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.000 | 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".