Effects of van der Waals interactions on the nonlinear vibration of multi-layered graphene sheets
Bibliographic record
Abstract
Abstract This paper is concerned with the forced nonlinear vibration of multi-layered graphene sheets modelled at the atomic level by the lattice structure approach. In this, the covalent bond between two carbon atoms is assumed as a structural member with prescribed physical and material properties. An atom is treated as a nodal point with its own mass and six degrees of freedom. The highly nonlinear van der Waals interaction between adjacent graphene layers is fully incorporated in the model by placing it in the force vector. This adjustment significantly reduces the computational hardships due to nonlinearity and increases the efficiency of the method. Newmark's direct integration method is modified to address the nonlinearity in the load vector and used for the solution of the matrix equation governing the motion of the multi-layered graphene sheet. Double-layered square graphene with simply supported and clamped boundary conditions is analysed to examine the out-of-plane and in-plane vibrational characteristics. Also, in order to illustrate the applicability of the numerical method, analyses are carried out with the first- and second-order Taylor series approximations of the van der Waals interactions, influence of which is found to be quite significant in the bending modes of vibration, but it essentially does not have a role in the in-plane modes. The numerical method developed herein is quite appropriate with reference to the structural formation at the atomic scale and also more efficient than previous computational approaches by others.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".