Free Vibration of Single Layer Graphene Sheets: Lattice Structure Versus Continuum Plate Theories
Bibliographic record
Abstract
Prospect of applications of graphene sheets in composites and other advanced materials have drawn attention from a broad spectrum of research fields. This paper deals with the methods to find mechanical properties of such nanoscale structures. First, the lattice structure method with the Poisson’s ratio of 0.16 and the thickness of 3.4 Å is used to obtain the Young’s moduli for the in-plane and out-of-plane deformation states. This method has the accuracy of molecular dynamics simulations and efficiency of the finite element method. The graphene sheet is modeled as a plane grid of carbon atoms taken as the nodal points, each of which carries the mass of the carbon atom and is assigned as a six degrees of freedom. The covalent bond between two adjacent carbon atoms is treated as an extremely stiff frame element with all three axial, bending, and torsional stiffness components. Subsequently, the computed Young’s moduli, approximately 0.11 TPa for bending and 1.04 TPa for the in-plane condition, are used for studying the vibrational behaviors of graphene sheets by the continuum plate theory. The natural frequencies and corresponding mode shapes of various shaped single layer graphene sheet ), such as rectangular, skewed, and circular, are computed by the two methods which are found to yield very close results. Results of the well-established continuum plate theory are very consistent with the lattice structure method, which is based on accurate interatomic forces.
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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 | 0.001 |
| 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 | 0.000 |
| 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".