A Dynamic Finite Element for Coupled Extensional-Torsional Vibration of Uniform Composite Thin-Walled Beams
Bibliographic record
Abstract
A Dynamic Finite Element (DFE) formulation for the free vibration analysis of extension-torsion coupled uniform composite thin-walled beams is presented. Employing the exact solutions of the differential equations governing the uncoupled vibrations of a uniform beam element, the analytical expressions for extensional and torsional dynamic trigonometric shape functions are derived. By exploiting the principle of virtual work and the frequency-dependent shape functions, the element dynamic stiffness matrix is developed. The application of the theory is demonstrated by a Circumferentially Uniform Stiffness (CUS) composite circular tube for which the influence of ply fibre-angle on the natural frequencies is studied. A variety of CUS configurations are studied and the correctness of the theory and the superiority of the proposed DFE over the conventional FEM methods are confirmed by numerical checks and the published results.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".