Atomic lattice structure and continuum plate theories for the vibrational characteristics of graphenes
Bibliographic record
Abstract
This paper is concerned with the equivalent extensional and flexural rigidities of a single layer graphene sheet by treating it as a plane lattice structure made of tightly packed carbon atoms into an array of honeycomb-shaped cells. Each carbon atom is modeled as a node with concentrated atomic mass and prescribed six degrees of freedom. The covalent bond between adjacent carbon atoms provides axial, bending, and torsional stiffness. Using the Poisson’s ratio of 0.16 and thickness of 3.4 Å, the equivalent Young’s moduli are found to be approximately 0.112 TPa for bending and in the range of 1.03–1.04 TPa for in-plane modes. Subsequently, the graphene structure is simulated by a classical plate with prescribed geometric and mechanical properties. The in-plane and out-of-plane free vibration analyses of the rectangular plate provide the natural frequencies and associated mode shapes. Results are compared with eigen analyses of the lattice structure model for different sizes of graphene. Examples are considered to show close agreement in the results from these two methods. Mode shapes reveal that the lattice structure model shows symmetry about the horizontal and vertical axes and also about the diagonals.
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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) | 0.000 | 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".