Vibration Analysis of Composite Wings Undergoing Material and Geometrical Couplings: A Dynamic Finite Element Formulation
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Bibliographic record
Abstract
The differential equations governing Geometric-Materially coupled torsion-flexural vibrations of laminated composite wings are first reviewed. Based on the finite element methodology (FEM), Euler-Bernoulli and St-Venant beam theories, the Dynamic Trigonometric Shape Functions (DTSFs) for the beam’s uncoupled displacements are thereafter derived. Exploiting the Principle of Virtual Work (PVW) and interpolating the variables based on the DTSF, the Dynamic Finite Element (DFE) formulations for uniform beams’ coupled vibrations are first developed. The variable geometrical and mechanical parameters are then incorporated in the formulation. The applicability of the DFE method is then demonstrated by two illustrative examples where a Wittrick-Williams root counting technique is used to find the systems’ natural frequencies. The proposed DFE approach can also be advantageously extended to incorporate more complexities, further coupling as well as other geometrical and mechanical parameters in the formulation.
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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 | 0.001 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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