Divergence and flutter analyses of functionally graded porous trapezoidal plates reinforced with graphene platelets under thermal loading
Bibliographic record
Abstract
In this article, the divergence and flutter behaviors of functionally graded (FG) porous trapezoidal plates reinforced with graphene platelets (GPLs) subjected to the supersonic airflow and thermal loading are investigated. It is assumed that porosity and graphene platelets are distributed in the thickness direction according to the functionally graded distributions. The material properties of FG porous reinforced with graphene platelets are estimated to be temperature-dependent. Three types of temperature distributions as uniform, linear and nonlinear temperature distributions in the thickness direction are considered. Using Hamilton’s principle, the governing equations of motion are derived in the Cartesian coordinates based on the first order shear deformation theory (FSDT) as well as the linear piston theory. Also, the linear stability or divergence equations are obtained according to the principle of minimum total potential energy and adjacent equilibrium criterion. Using a mapping, the divergence and flutter partial differential equations and the associated boundary conditions in the Cartesian coordinates are converted to ones in the trapezoidal coordinates. Applying the generalized differential quadrature (GDQ) method and the state space technique, the transformed equations with the corresponding boundary conditions are solved to find the critical flutter aerodynamic pressure as well as the critical divergence temperature difference. The effects of various parameters such as porosity coefficient, symmetric and asymmetric porosity distribution, GPL distribution patterns, temperature differences and boundary conditions are studied on the stability region. The present results of this study can be used to design and manufacture the advanced aerospace vehicles at supersonic speeds and temperature changes.
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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 | 0.000 |
| 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 | 0.001 |
| 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 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".