Vibration Analysis of Composite Wings Undergoing Material and Geometrical Couplings: A Dynamic Finite Element Formulation
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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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 | 0.001 | 0.000 |
| Research integrity | 0.001 | 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".